Light-emitting device

ABSTRACT

The present embodiment relates to a light emitting device having a structure capable of removing zero order light from output light of an S-iPM laser. The light emitting device includes a semiconductor light emitting element and a light shielding member. The semiconductor light emitting element includes an active layer, a pair of cladding layers, and a phase modulation layer. The phase modulation layer has a basic layer and a plurality of modified refractive index regions, each of which is individually disposed at a specific position. The light shielding member has a function of passing through a specific optical image output along an inclined direction and shielding zero order light output along a normal direction of a light emitting surface.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation-In-Part application of patentapplication Ser. No. 16/323,625 claiming the benefit of priority of theJapanese Patent Application No. 2016-157792 filed on Aug. 10, 2016 andfurther claims the benefit of priority of the Japanese PatentApplication No. 2018-110112 filed on Jun. 8, 2018, the entire contentsof which are incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a light emitting device.

BACKGROUND ART

The semiconductor light emitting element described in Patent Document 1includes an active layer, a pair of cladding layers sandwiching theactive layer, and a phase modulation layer provided optically coupled tothe active layer. The phase modulation layer has a basic layer and aplurality of modified refractive index regions each having a differentrefractive index from a refractive index of the basic layer. In the caseof setting a square lattice on the phase modulation layer, each of themodified refractive index regions (main holes) is disposed so as tocoincide with the center point (lattice point) of a corresponding region(having a square shape) in the square lattice. An auxiliary modifiedrefractive index region (auxiliary hole) is provided around the modifiedrefractive index region, and light having a predetermined beam patterncan be emitted.

CITATION LIST Patent Literature

Patent Document 1: International Publication No. 2014/136962

SUMMARY OF INVENTION Technical Problem

As a result of examining the conventional semiconductor light emittingelement, the inventors of the present invention have found the followingproblems. That is, a semiconductor light emitting element is under studywhich outputs an arbitrary optical image by controlling phase spectrumand intensity spectrum of light emitted from a plurality oftwo-dimensionally arranged light emitting points. As one structure ofsuch a semiconductor light emitting element, a lower cladding layer, anactive layer, and an upper cladding layer are provided on asemiconductor substrate, and between the lower cladding layer and theactive layer or between the active layer and the upper cladding layer, aphase modulation layer is provided. The phase modulation layer includesa basic layer and a plurality of modified refractive index regions eachhaving a different refractive index from a refractive index of the basiclayer. When a virtual square lattice is set in a thickness direction ofthe phase modulation layer on a vertical surface, the position of thecenter of gravity of the modified refractive index region allocated toeach of a plurality of square regions forming the square lattice shiftsfrom a lattice point position of the square region allocated accordingto an optical image to be generated. Such a semiconductor light emittingelement is called an S-iPM (Static-integrable Phase Modulating) laserand outputs a beam for forming an optical image having a two-dimensionalarbitrary shape along a direction (normal direction) perpendicular to amain surface of the semiconductor substrate and a direction having apredetermined spread angle with respect to the normal direction.

However, in addition to a signal light which is a desired output opticalimage, zero order light is output from the above-described semiconductorlight emitting element. The zero order light is a light output in adirection perpendicular to the main surface of a semiconductor substrate(that is, a direction perpendicular to the light emitting surface) andis not normally used in the S-iPM laser. Therefore, in order to obtain adesired output optical image, the zero order light becomes noise light,and therefore it is desirable to remove the zero order light from anoptical image.

To solve the above-described problems, an object of the presentinvention is to provide a light emitting device having a structurecapable of removing zero order light from output light of an S-iPMlaser.

Solution to Problem

In order to solve the above-described problem, a light emitting deviceaccording to an embodiment of the present invention includes, forexample, a semiconductor light emitting element and a light shieldingmember. The semiconductor light emitting element has a light emittingsurface and outputs an optical image having an arbitrary shape along anormal direction of the light emitting surface and an inclined directionhaving a predetermined inclination and a spread angle with respect tothe normal direction. The light shielding member is disposed such thatan axis orthogonal to the light emitting surface at a position of thecenter of gravity of the light emitting surface crosses a part of thelight shielding member. Further, the semiconductor light emittingelement includes an active layer, a pair of cladding layers sandwichingthe active layer, and a phase modulation layer provided between theactive layer and either a pair of the cladding layers and opticallycoupled to the active layer. The light shielding member is disposed soas to pass through a specific optical image output in an inclineddirection among the output optical images and to shield zero order lightoutput in a normal direction of the light emitting surface. The phasemodulation layer has a basic layer and a plurality of modifiedrefractive index regions each having a different refractive index from arefractive index of the basic layer. On the other hand, a method ofmanufacturing a semiconductor light emitting element includes first tofourth steps. In the first step, a lower cladding layer (one of a pairof the cladding layers) is provided on a substrate. In the second step,the active layer is provided on the lower cladding layer. In the thirdstep, an upper cladding layer (the other one of a pair of the claddinglayers) is provided on the active layer. The fourth step is performedbetween the first step and the second step or between the second stepand the third step, and the phase modulation layer is provided betweenthe lower cladding layer and the active layer or between the activelayer and the upper cladding layer. In the method of manufacturing thelight emitting device, a desired light emitting device can be obtainedby disposing, to the semiconductor light emitting element manufacturedin this way, the light shielding member such that the axis lineorthogonal to the light emitting surface at a position of the center ofgravity of the light emitting surface crosses a part of the lightshielding member.

In particular, in the light emitting device and the method ofmanufacturing the semiconductor light emitting element according to thepresent embodiment, the phase modulation layer is configured such thateach of a plurality of the modified refractive index regions isindividually disposed at a specific position. Specifically, the phasemodulation layer is formed such that, in an XYZ orthogonal coordinatesystem defined by a Z axis that coincides with a normal direction and anX-Y plane that coincides with one surface of the phase modulation layerincluding a plurality of modified refractive index regions and thatincludes mutually orthogonal X and Y axes, where a virtual squarelattice including M1 (integer of 1 or more)×N1 (integer of 1 or more)unit constituent regions R each having a square shape is set on the X-Yplane, in the unit constituent region R (x, y) on the X-Y planespecified by a coordinate component x (an integer of from 1 to M1) inthe X axis direction and a coordinate component y (an integer of from 1to N1) in the Y axis direction, the center of gravity G1 of the modifiedrefractive index region located in the unit constituent region R (x, y)is away from the lattice point O (x, y) which is the center of the unitconstituent region R (x, y), and a vector from the lattice point O (x,y) to the center of gravity G1 is oriented in a specific direction.

Advantageous Effects of Invention

According to the light emitting device and the method of manufacturingthe semiconductor light emitting element according to the presentembodiment, a zero order light can be removed from the output of a S-iPMlaser.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a perspective view illustrating a configuration of a lightemitting device according to an embodiment of the present invention.

FIG. 2 is a cross-sectional view illustrating a configuration of a laserelement.

FIG. 3 is a view illustrating a modification relating to a phasemodulation layer.

FIG. 4 is a plan view of a phase modulation layer.

FIG. 5 indicates a positional relationship of modified refractive indexregions in a phase modulation layer.

FIG. 6 is a plan view of an example in which a refractive indexsubstantially periodic structure of FIG. 4 is applied only in a specificregion of a phase modulation layer.

FIG. 7 is a view for explaining a relationship between an optical imageobtained by imaging an output beam pattern of a laser element and arotation angle distribution in a phase modulation layer.

FIGS. 8A and 8B are views for explaining points to be noted indetermining a rotation angle distribution from a result of Fouriertransform of an optical image and determining the arrangement ofmodified refractive index regions.

FIG. 9A is an image of an original pattern common to three specificaspects of a phase modulation layer. FIG. 9B is an image obtained byextracting an intensity distribution by performing two-dimensionalinverse Fourier transform on FIG. 9A. FIG. 9C is an image obtained byextracting a phase distribution by performing two-dimensional inverseFourier transform on FIG. 9A.

FIG. 10A is an image of a first configuration of a phase modulationlayer for realizing the phase distribution illustrated in FIG. 9C. FIG.10B is a predicted beam pattern obtained by Fourier transforming theentire modified refractive index regions.

FIG. 11 is a graph indicating an S/N ratio of an output beam patternaccording to a relationship between a filling factor and a distance r(a)in the first configuration of a phase modulation layer.

FIG. 12 is graphs indicating a relationship between the distance r(a)and the S/N ratio in the first configuration of a phase modulationlayer.

FIG. 13A is an image of a second configuration of a phase modulationlayer for realizing the phase distribution illustrated in FIG. 9C. FIG.13B is a predicted beam pattern obtained by Fourier transforming theentire modified refractive index regions.

FIG. 14 is a graph indicating an S/N ratio of an output beam patternaccording to a relationship between a filling factor and the distancer(a) in the second configuration of a phase modulation layer.

FIG. 15 is graphs indicating a relationship between the distance r(a)and the S/N ratio in the second configuration of the phase modulationlayer.

FIG. 16A is an image of a third configuration of a phase modulationlayer for realizing the phase distribution illustrated in FIG. 9C. FIG.16B is a predicted beam pattern obtained by Fourier transforming theentire modified refractive index regions.

FIG. 17 is a graph indicating an S/N ratio of an output beam patternaccording to a relationship between a filling factor and a distance r(a)in the third configuration of a phase modulation layer.

FIG. 18 is graphs indicating a relationship between the distance r(a)and the S/N ratio in the third configuration of a phase modulationlayer.

FIGS. 19A to 19C indicate examples of beam patterns (optical images)output from a laser element.

FIG. 20 is a view indicating conditions to be used for diffractioncalculation.

FIG. 21A is a diagram indicating a target image used for diffractioncalculation. FIGS. 21B and 21C are views illustrating phase distributionin a phase modulation layer in the case of the lattice spacing a=282 nmand 141 nm, with shade of color.

FIG. 22 is a graph indicating calculation results and indicatescorrelation between a distance d and a distance z in the case where adistance between one end on the Z axis on a diffraction image plane andthe Z axis is denoted by d (μm), and a distance between the diffractionimage surface and a light emitting surface 2 b is denoted by z (μm).

FIG. 23 illustrates a part of the diffraction image that is the basis ofthe graph of FIG. 22.

FIG. 24 illustrates a part of the diffraction image that is the basis ofthe graph of FIG. 22.

FIG. 25 illustrates a part of the diffraction image that is the basis ofthe graph of FIG. 22.

FIG. 26 illustrates a part of the diffraction image that is the basis ofthe graph of FIG. 22.

FIG. 27 illustrates a part of the diffraction image that is the basis ofthe graph of FIG. 22.

FIG. 28 is a graph indicating the correlation between a product (d×L) ofthe distance d and an electrode size L and the distance z.

FIG. 29 is a schematic diagram of a positional relationship between alight emitting surface and a light shielding member.

FIG. 30 is an enlarged diagram of the vicinity of an intersection of aZ-axis side edge of a first optical image portion B2 and a first opticalimage portion B2 side edge of a zero order light B1.

FIG. 31 is a graph indicating a change in the beam radius at the beamwaist of the Gaussian beam.

FIGS. 32A to 32D are plan views illustrating concrete examples of thearrangement of light shielding members.

FIGS. 33A to 33D are plan views illustrating concrete examples of thearrangement of light shielding members.

FIG. 34 is a plan view of a phase modulation layer according to amodification of the present invention.

FIGS. 35A to 35C are plan views illustrating examples of shapes in theX-Y plane of the modified refractive index region.

FIGS. 36A and 36B are plan views illustrating examples of shapes in theX-Y plane of the modified refractive index regions.

FIG. 37 illustrates a configuration of a light emitting device accordingto a third modification.

FIG. 38 is a diagram for explaining coordinate transformation fromspherical coordinates (d1, θ_(tilt), θ_(rot)) to coordinates (x, y, z)in an XYZ orthogonal coordinate system.

DESCRIPTION OF EMBODIMENTS Description of Embodiments of the PresentInvention

First, the contents of an embodiment of the present invention will beindividually listed and described individually.

(1) A light emitting device according to the embodiment of the presentinvention includes a semiconductor light emitting element and a lightshielding member as an aspect thereof. The semiconductor light emittingelement has a light emitting surface and outputs an optical image havingan arbitrary shape along a normal direction of the light emittingsurface and an inclined direction having a predetermined inclination anda spread angle with respect to the normal direction. The light shieldingmember is disposed such that an axis orthogonal to the light emittingsurface at a position of the center of gravity of the light emittingsurface crosses a part of the light shielding member. Further, thesemiconductor light emitting element includes an active layer, a pair ofcladding layers sandwiching the active layer, and a phase modulationlayer provided between the active layer and either a pair of thecladding layers and optically coupled to the active layer. The lightshielding member is disposed so as to pass through a specific opticalimage output in an inclined direction among the output optical imagesand to shield zero order light output in a normal direction of the lightemitting surface. The phase modulation layer has a basic layer and aplurality of modified refractive index regions each having a differentrefractive index from a refractive index of the basic layer. On theother hand, a method of manufacturing a semiconductor light emittingelement includes first to fourth steps. In the first step, a lowercladding layer (one of a pair of the cladding layers) is provided on asubstrate. In the second step, the active layer is provided on the lowercladding layer. In the third step, an upper cladding layer (the otherone of a pair of the cladding layers) is provided on the active layer.The fourth step is performed between the first step and the second stepor between the second step and the third step, and the phase modulationlayer is provided between the lower cladding layer and the active layeror between the active layer and the upper cladding layer. In the methodof manufacturing the light emitting device, a desired light emittingdevice can be obtained by disposing, to the semiconductor light emittingelement manufactured in this way, the light shielding member such thatthe axis line orthogonal to the light emitting surface at a position ofthe center of gravity of the light emitting surface crosses a part ofthe light shielding member.

In particular, in the light emitting device and the method ofmanufacturing the semiconductor light emitting element according to thepresent embodiment, the phase modulation layer is configured such thateach of a plurality of the modified refractive index regions isindividually disposed at a specific position. Specifically, as a firstprecondition, in an XYZ orthogonal coordinate system defined by a Z axisthat coincides with a normal direction and an X-Y plane that includes Xand Y axes orthogonal to each other and coincides with one face of thephase modulation layer including a plurality of modified refractiveindex regions, a virtual square lattice including M1 (an integer of 1 ormore)×N1 (an integer of 1 or more) unit constituent regions R eachhaving a square shape is set on the X-Y plane. At this time, in the unitconstituent region R (x, y) on the X-Y plane specified by a coordinatecomponent x (an integer of from 1 to M1) in the X axis direction and acoordinate component y (an integer of from 1 to N1) in the Y-axisdirection, a phase modulation layer is formed such that the center ofgravity G1 of the modified refractive index region located in the unitconstituent region R (x, y) is away from the lattice point O (x, y)which is the center of the unit constituent region R (x, y), and avector from the lattice point O (x, y) to the center of gravity G1 isoriented in a specific direction.

In the semiconductor light emitting element having the above-describedstructure, the phase modulation layer optically coupled to the activelayer includes a basic layer and a plurality of modified refractiveindex regions each being embedded in the basic layer and having arefractive index different from a refractive index of the basic layer.Further, in the unit constituent region R (x, y) constituting a virtualsquare lattice, the center of gravity G1 of the corresponding modifiedrefractive index region is disposed away from the lattice point O (x,y). Further, a direction of the vector from the lattice point O to thecenter of gravity G1 is individually set for each unit constituentregion R. In such a configuration, depending on the direction of thevector from the lattice point O to the center of gravity G1 of thecorresponding modified refractive index region, that is, a phase of beamchanges according to an angular position around the lattice point of thecenter of gravity G1 of the modified refractive index region. Asdescribed above, according to the present embodiment, it is possible tocontrol the phase of a beam output from each of the modified refractiveindex regions only by changing a position of the center of gravity inthe modified refractive index region. A beam pattern (beam group formingan optical image) formed as a whole can be controlled to a desiredshape. At this time, the lattice point in the virtual square lattice maybe located outside the modified refractive index region, and the latticepoint may be located inside the modified refractive index region.

That is, the semiconductor light emitting element applicable to thepresent embodiment is an S-iPM laser and can output an optical imagehaving an arbitrary shape (for example, a beam pattern formed on atwo-dimensional plane) along a normal direction of the light emittingsurface and an inclined direction having a predetermined inclination anda spread angle with respect to the normal direction. Furthermore, alight shielding member is disposed such that an axis orthogonal at aposition of the center of gravity of a light emitting surface(coinciding with the Z axis) crosses a part of the light shieldingmember, and the light shielding member functions to shield zero orderlight while passing through a specific optical image output along theinclined direction. As a result, the zero order light can be removedfrom the output of the S-iPM laser.

(2) As an aspect of the present embodiment, where a lattice constant ofa virtual square lattice (substantially corresponding to a latticespacing) is a, it is preferable that the distance r between the centerof gravity G1 of a modified refractive index region located in the unitconstituent region R (x, y) and the lattice point O (x, y) satisfies0≤r≤0.3a. Further, in the above-described light emitting device, as anoriginal image (optical image before two-dimensional inverse Fourierreturn) represented by the beam pattern emitted from the semiconductorlight emitting element, at least one of a spot, a straight line, across, a line drawing, a lattice pattern, photographs, striped patterns,computer graphics, and letters is preferably included.

(3) In an aspect of the present embodiment, in addition to the firstprecondition, as the second precondition, it is assumed that thecoordinates (x, y, z) in the XYZ orthogonal coordinate system satisfiesthe relationship expressed by the following expressions (1) to (3), asillustrated in FIG. 38, with respect to the spherical coordinates (d1,θ_(rot)) defined by the length d1 of a moving radius, the inclinationangle θ_(tilt) from the Z axis, and the rotation angle θ_(rot) from theX axis specified on the X-Y plane. FIG. 38 is a diagram for explainingthe coordinate transformation from the spherical coordinates (d1,θ_(rot)) to the coordinates (x, y, z) in the XYZ orthogonal coordinatesystem, and a designed optical image on a predetermined plane set in theXYZ orthogonal coordinate system which is a real space is expressed.Where a beam pattern corresponding to an optical image output from asemiconductor light emitting element is a set of bright points directedin directions defined by angles θ_(tilt) and θ_(rot), the anglesθ_(tilt) and θ_(rot) are converted into a coordinate value k_(x) on theKx axis corresponding to the X axis which is a normalized wave numberdefined by the following formula (4) and a coordinate value k_(y) on theKy axis orthogonal to the Kx axis corresponding to the Y axis which is anormalized wave number defined by the following formula (5). Thenormalized wavenumber means a wavenumber normalized with a wavenumbercorresponding to a lattice spacing of a virtual square lattice taken as1.0. At this time, in a wavenumber space defined by the Kx axis and theKy axis, a specific wavenumber range including a beam patterncorresponding to an optical image includes M2 (an integer of 1 ormore)×N2 (an integer of 1 or more) image regions FR. Note that theinteger M2 does not have to match the integer M1. Likewise, the integerN2 does not have to match the integer N1. Further, formulas (4) and (5)are disclosed in, for example, Y. Kurosaka et al., “Effects ofnon-lasing band in two-dimensional photonic-crystal lasers clarifiedusing omnidirectional band structure,” Opt. Express 20, 21773-21783(2012).

$\begin{matrix}{x = {d\; 1\;\sin\;\theta_{tilt}\cos\;\theta_{rot}}} & (1) \\{y = {d\; 1\;\sin\;\theta_{tilt}\sin\;\theta_{rot}}} & (2) \\{z = {d\; 1\;\cos\;\theta_{tilt}}} & (3) \\{k_{x} = {\frac{a}{\lambda}\sin\;\theta_{tilt}\cos\;\theta_{rot}}} & (4) \\{k_{y} = {\frac{a}{\lambda}\sin\;\theta_{tilt}\sin\;\theta_{rot}}} & (5)\end{matrix}$a: Lattice constant of vertical square latticeλ: Oscillation wavelength of semiconductor light emitting element

As a third precondition, in a wavenumber space, a complex amplitude F(x, y) obtained

by performing two-dimensional inverse Fourier transform to transformeach of the image regions FR (k_(x), k_(y)) specified by a coordinatecomponent k_(x) (an integer of from 0 to M2−1) in the Kx axis directionand a coordinate component k_(y) (an integer of from 0 to N2−1) in theKy axis direction to the unit constituent region R (x, y) on the X-Yplane specified by a coordinate component x (an integer of from 1 to M1)in the X axis direction and a coordinate component y (an integer of from1 to N1) in the Y axis direction is expressed by the following formula(6) with j being an imaginary unit: Further, this complex amplitude F(x, y) is defined by the following formula (7) where the amplitude termis denoted by A (x, y) and the phase term is denoted by P (x, y).Furthermore, as a fourth precondition, the unit constituent region R (x,y) is defined by s and t axes mutually orthogonal at the lattice point O(x, y) that is parallel to the X axis and the Y axis and is the centerof the unit constituent region R (x, y).

$\begin{matrix}{{F\left( {x,y} \right)} = {\sum\limits_{k_{x} = 0}^{{M\; 2} - 1}{\sum\limits_{k_{y} = 0}^{{N\; 2} - 1}{{{FR}\left( {k_{x},k_{y}} \right)}{\exp\left\lbrack {j\; 2{\pi\left( {{\frac{k_{x}}{M\; 2}x} + {\frac{k_{y}}{N\; 2}y}} \right)}} \right\rbrack}}}}} & (6) \\{{F\left( {x,y} \right)} = {{A\left( {x,y} \right)} \times {\exp\left\lbrack {{jP}\left( {x,y} \right)} \right\rbrack}}} & (7)\end{matrix}$

Under the above-described first to fourth preconditions, the phasemodulation layer is configured to satisfy the following first and secondconditions. That is, the first condition is that, in the unitconstituent region R (x, y), one of a plurality of the modifiedrefractive index regions corresponds to a state in which the center ofgravity G1 is disposed away from the lattice point O (x, y). Further,under, the second condition, the corresponding modified refractive indexregion is disposed in the unit constituent region R (x, y) such that theangle φ (x, y) formed by the line segment connecting the lattice point O(x, y) and the center of gravity G1 of the corresponding modifiedrefractive index region and the s axis satisfies the followingrelationship in a state in which the line segment length r (x, y) fromthe lattice point O (x, y) to the center of gravity G1 of thecorresponding modified refractive index region is set to a common valuein each of M1×N1 unit constituent regions R:φ(x,y)=C×P(x,y)+B

C: Proportional constant, for example 180°/π

B: Arbitrary constant, for example 0

In the semiconductor light emitting element having the above-describedstructure, in the phase modulation layer, the distance r between thecenter (lattice point) of each unit constituent region constituting avirtual square lattice and the center of gravity G1 of the correspondingmodified refractive index region is preferably constant over the entirephase modulation layer. Thereby, in the case where the phasedistribution (the distribution of the phase term P (x, y) in the complexamplitude F (x, y) assigned to the unit constituent region R (x, y)) inthe entire phase modulation layer is equally distributed from 0 to 2π(rad), on average, the center of gravity of the modified refractiveindex region coincides with the lattice point of the unit constituentregion R in a square lattice. Therefore, since the two-dimensionaldistributed Bragg diffraction effect in the above-described phasemodulation layer approaches the two-dimensional distributed Braggdiffraction effect in the case where the modified refractive indexregion is disposed on each lattice point of the square lattice, astanding wave can be easily formed, and reduction in threshold currentfor oscillation can be expected.

(4) As an aspect of the present embodiment, a distance from a lightemitting surface to a light shielding member is denoted by z, a distancefrom an axis to the nearest edge of the light shielding member on areference plane including the axis is denoted by Wa, the beam width ofzero order light at a point of the distance z is denoted by W_(z), thewidth of the light emitting surface defined on the reference plane isdenoted by L, an angle formed by an axial side edge of a specificoptical image and the axis on the reference plane is denoted by θ_(PB),and the emission wavelength of the active layer is denoted by λ, thedistance z is preferably longer than z_(sh) defined by the followingformula (8):

$\begin{matrix}{z_{sh} = \frac{W_{z} + L}{2\tan\;\theta_{PB}}} & (8)\end{matrix}$

In addition, the distance Wa is preferably longer than half of W_(z)defined by the following formula (9).

$\begin{matrix}{{W_{Z} = {\frac{4\lambda}{\pi\; L}z\mspace{14mu}\left( {{{where}\mspace{14mu} z} \geq z_{0}} \right)}}{W_{Z} = {\sqrt{2}L\mspace{14mu}\left( {{{where}\mspace{14mu} z} < z_{0}} \right)}}} & (9)\end{matrix}$

However, Z₀ in the above formula (9) is a numerical value defined by thefollowing formula (10).

$\begin{matrix}{z_{0} = {\frac{\pi}{\lambda}\left( \frac{L}{2} \right)^{2}}} & (10)\end{matrix}$

Thereby, the light shielding member can effectively shield the zeroorder light.

(5) As an aspect of the present embodiment, the optical image mayinclude a first optical image portion output in a first directioninclined with respect to an axis and a second optical image portionoutput in a second direction symmetrical to the first direction withrespect to the axis and rotationally symmetric to the first opticalimage portion with respect to the axis. In this case, the lightshielding member is disposed to further shield the second optical imageportion. As described above, according to the present aspect, it ispossible to effectively remove unnecessary second optical image portionswhen the first optical image portion is the above-described specificoptical image.

(6) In one aspect of the present embodiment, the light shielding memberpreferably includes a light absorbing material. When the light shieldingmember reflects the zero order light, the reflected light again entersthe semiconductor light emitting element, which may affect the operationinside the semiconductor light emitting element. By including the lightabsorbing material in the light shielding member, it is possible toabsorb the zero order light and prevent the zero order light fromentering the semiconductor light emitting element again.

(7) As an aspect of the present embodiment, the light emitting devicemay include a plurality of semiconductor light emitting elements eachhaving a light emitting surface, a light shielding member, and a drivecircuit for individually driving a plurality of the semiconductor lightemitting elements. Each of a plurality of the semiconductor lightemitting elements outputs an optical image having an arbitrary shapealong a normal direction of the light emitting surface and an inclineddirection having a predetermined inclination and a spread angle withrespect to the normal direction. The light shielding member is disposedsuch that each of the axis lines orthogonal to the light emittingsurface and a part the light shielding member cross each other at thecenter of gravity of the light emitting surface of each of a pluralityof the semiconductor light emitting elements. Further, each of aplurality of the semiconductor light emitting elements includes anactive layer, a pair of cladding layers sandwiching the active layer,and a phase modulation layer provided between the active layer andeither a pair of the cladding layers and optically coupled to the activelayer. The light shielding member is disposed so as to pass through aspecific optical image output in an inclined direction among the outputoptical images and to shield zero order light output in a normaldirection of the light emitting surface. In each of a plurality of thesemiconductor light emitting elements, the phase modulation layer has abasic layer and a plurality of modified refractive index regions eachhaving a different refractive index from a refractive index of the basiclayer.

Further, the phase modulation layers of each of a plurality of thesemiconductor light emitting elements are configured as follows. Thatis, in each of a plurality of the semiconductor light emitting elements,in an XYZ orthogonal coordinate system defined by a Z axis thatcoincides with a normal direction and an X-Y plane that includes X and Yaxes orthogonal to each other and coincides with one surface of thephase modulation layer including a plurality of modified refractiveindex regions, a virtual square lattice including M1 (an integer of 1 ormore)×N1 (an integer of 1 or more) unit constituent regions R eachhaving a square shape is set on the X-Y plane. At this time, a phasemodulation layer is formed such that, in the unit constituent region R(x, y) on the X-Y plane specified by a coordinate component x (aninteger of from 1 to M1) in the X axis direction and a coordinatecomponent y (an integer of from 1 to N1) in the Y axis direction, thecenter of gravity G1 of the modified refractive index region located inthe unit constituent region R (x, y) is away from the lattice point O(x, y) which is the center of the unit constituent region R (x, y), andthe vector from the lattice point O (x, y) to the center of gravity G1is oriented in a specific direction. As described above, the lightemitting device includes a plurality of individually drivensemiconductor light emitting elements, such that it is possible toextract only a desired optical image from each of the semiconductorlight emitting elements. With this, it is possible to suitably realize ahead up display or the like by appropriately driving required elementsfor a module in which semiconductor light emitting elementscorresponding to a plurality of patterns are aligned in advance.

(8) As an aspect of the present embodiment, it is preferable that eachof a plurality of semiconductor light emitting elements includes any oneof a semiconductor light emitting element that outputs an optical imagein a red wavelength range, a semiconductor light emitting element thatoutputs an optical image in a blue wavelength range, and a semiconductorlight emitting element that outputs an optical image in a greenwavelength range. In this case, a color head up display or the like canbe suitably realized.

As described above, each aspect listed in “Description of Embodiments ofthe Present Invention” can be applied to all of the remaining aspects orto all combinations of these remaining aspects.

Details of Embodiment of Present Invention

Hereinafter, a specific structure of the light emitting device accordingto the present embodiment will be described in detail with reference tothe attached drawings. It should be noted that the present invention isnot limited to these illustrative examples, but is indicated by thescope of the claims, and it is intended to include meanings equivalentto the claims and all changes within the scope. In the description ofthe drawings, the same elements are denoted by the same referencenumerals, and redundant explanations are omitted.

FIG. 1 is a perspective view of a configuration of a light emittingdevice 1A according to an embodiment of the present invention. The lightemitting device 1A includes a laser element 2A as a semiconductor lightemitting element and a light shielding member 3 optically coupled to thelight emitting surface 2 b of the laser element 2A. An XYZ orthogonalcoordinate system is defined by a Z axis passing through the center ofthe laser element 2A (the position of the center of gravity of the lightemitting surface 2 b) and extending in the thickness direction of thelaser element 2A, and an X-Y plane that is a plane orthogonal to the Zaxis and that coincides with one surface of the phase modulation layer15A including modified refractive index regions 15 b and includesmutually orthogonal X axis and Y axis. The laser element 2A is an S-iPMlaser that forms a standing wave along the X-Y plane and outputs aphase-controlled plane wave in the Z-axis direction. As will bedescribed later, the laser element 2A outputs a two dimensional opticalimage having an arbitrary shape along a normal direction (that is theZ-axis direction) of the light emitting surface 2 b and an inclineddirection having a predetermined inclination and a spread angle withrespect to the normal direction. The light shielding member 3 isdisposed to face the light emitting surface 2 b of the laser element 2Aand shields zero order light included in a beam pattern output from thelaser element 2A. Hereinafter, the configurations of the laser element2A and the light shielding member 3 will be described in detail.

FIG. 2 is a cross-sectional view of a laminate configuration of thelaser element 2A. As illustrated in FIGS. 1 and 2, the laser element 2Aincludes an active layer 12 provided on a semiconductor substrate 10, apair of cladding layers 11 and 13 sandwiching the active layer 12, and acontact layer 14 provided on the cladding layer 13 (upper cladding). Thesemiconductor substrate 10 and each of the layers 11 to 14 include acompound semiconductor such as a GaAs-based semiconductor, an InP-basedsemiconductor, or a nitride-based semiconductor. An energy band gap ofthe cladding layer 11 (lower cladding layer) and an energy band gap ofthe cladding layer 13 are larger than an energy band gap of the activelayer 12. Thickness directions (lamination directions) of thesemiconductor substrate 10 and each of the layers 11 to 14 coincide withthe Z axis direction.

The laser element 2A further includes a phase modulation layer 15Aoptically coupled to the active layer 12. In the present embodiment, thephase modulation layer 15A is provided between the active layer 12 andthe cladding layer 13. If necessary, an optical guide layer may beprovided between at least one of the active layer 12 and the claddinglayer 13 and the active layer 12 and the cladding layer 11. When theoptical guide layer is provided between the active layer 12 and thecladding layer 13, the phase modulation layer 15A is provided betweenthe cladding layer 13 and the optical guide layer. The thicknessdirection of the phase modulation layer 15A coincides with the Z axisdirection.

As illustrated in FIG. 3, the phase modulation layer 15A may be providedbetween the cladding layer 11 and the active layer 12. Furthermore, whenthe optical guide layer is provided between the active layer 12 and thecladding layer 11, the phase modulation layer 15A is provided betweenthe cladding layer 11 and the optical guide layer.

The phase modulation layer 15A includes the basic layer 15 a including afirst refractive index medium and multiple modified refractive indexregions 15 b including a second refractive index medium having arefractive index different from that of the first refractive indexmedium and arranged in the basic layer 15 a. A plurality of the modifiedrefractive index regions 15 b includes a substantially periodicstructure. Where an effective refractive index of the phase modulationlayer 15A is denoted by n, the wavelength λ₀ (=a×n, a is a latticespacing) selected by the phase modulation layer 15A is included withinan emission wavelength range of the active layer 12. The phasemodulation layer (diffraction lattice layer) 15A can select thewavelength λ₀ out of the emission wavelength of the active layer 12 andoutput the light of the selected wavelength to the outside. The laserlight incident into the phase modulation layer 15A forms a predeterminedmode corresponding to the arrangement of the modified refractive indexregion 15 b in the phase modulation layer 15A, and is output as a laserbeam having a desired pattern from a surface of the laser element 2A(light emitting surface 2 b) to the outside.

The laser element 2A further includes an electrode 16 provided on thecontact layer 14 and an electrode 17 provided on a back surface 10 b ofthe semiconductor substrate 10. The electrode 16 is in ohmic contactwith the contact layer 14, and the electrode 17 is in ohmic contact withthe semiconductor substrate 10. Furthermore, the electrode 17 has anopening 17 a. A portion other than the electrode 16 on the contact layer14 is covered with a protective film 18 (refer to FIG. 2). Note that thecontact layer 14 not in contact with the electrode 16 may be removed. Aportion (including the inside of the opening 17 a) other than theelectrode 17 of the back surface 10 b of the semiconductor substrate 10is covered with an antireflection film 19. The antireflection film 19 ina region other than the opening 17 a may be removed.

When a driving current is supplied between the electrode 16 and theelectrode 17, recombination of electrons and holes occurs in the activelayer 12 (light emission). The electrons and holes contributing to thelight emission and the generated light are efficiently confined betweenthe cladding layer 11 and the cladding layer 13.

The laser light emitted from the active layer 12 is incident inside thephase modulation layer 15A and forms a predetermined mode correspondingto the lattice structure inside the phase modulation layer 15A. Thelaser light scattered and emitted in the phase modulation layer 15A isreflected by the electrode 16 and is emitted from the back surface 10 bthrough the opening 17 a to the outside. At this time, the zero orderlight of the laser light is emitted in a direction perpendicular to amain surface 10 a. On the other hand, a signal light of the laser lightis emitted along a direction perpendicular to the main surface 10 a(normal direction) and a direction having a predetermined spread anglewith respect to the normal direction. It is the signal light that formsa desired optical image (specific optical image), and the zero orderlight is not used in the present embodiment.

As an example, the semiconductor substrate 10 is a GaAs substrate, andthe cladding layer 11, the active layer 12, the phase modulation layer15A, the cladding layer 13, and the contact layer 14 are a compoundsemiconductor layer that includes elements contained in the groupconsisting of group III elements Ga, Al, and In and group V element As.As a specific example, the cladding layer 11 is an AlGaAs layer, theactive layer 12 has a multiple quantum well structure (barrier layer:AlGaAs/well layer: InGaAs), the basic layer 15 a of the phase modulationlayer 15A is GaAs, the modified refractive index region 15 b is a hole,the cladding layer 13 is an AlGaAs layer, and the contact layer 14 is aGaAs layer.

In AlGaAs, an energy band gap and a refractive index can be easilychanged by changing an Al composition ratio. In Al_(x)Ga_(1-x)As, whendecreasing (increasing) the composition ratio X of Al having arelatively small atomic radius, the energy band gap positivelycorrelated with this decreases (increases). In addition, if In having alarge atomic radius is mixed with GaAs to form InGaAs, the energy bandgap becomes small. That is, the Al composition ratio of the claddinglayers 11 and 13 is larger than the Al composition ratio of the barrierlayer (AlGaAs) of the active layer 12. The Al composition ratio of thecladding layers 11 and 13 is set to, for example, 0.2 to 0.4, and is 0.3in one example. The Al composition ratio of the barrier layer of theactive layer 12 is set to, for example, 0.1 to 0.15, and is 0.1 in oneexample.

As another example, the semiconductor substrate 10 is an InP substrate,and the cladding layer 11, the active layer 12, the phase modulationlayer 15A, the cladding layer 13, and the contact layer 14 are made of acompound semiconductor, for example, an InP-based compoundsemiconductor, which is not constituted only by an element contained inthe group consisting of group III elements Ga, Al, and In and group Velement As. As a specific example, the cladding layer 11 is an InPlayer, the active layer 12 has a multiple quantum well structure(barrier layer: GaInAsP/well layer: GaInAsP), the basic layer 15 a ofthe phase modulation layer 15A is GaInAsP, the modified refractive indexregion 15 b is a hole, the cladding layer 13 is an InP layer, and thecontact layer 14 is a GaInAsP layer.

Further, as another example, the semiconductor substrate 10 is a GaNsubstrate, and the cladding layer 11, the active layer 12, the phasemodulation layer 15A, the cladding layer 13, and the contact layer 14are a compound semiconductor layer, for example, made of a nitride-basedcompound semiconductor. The compound semiconductor layer is notconstituted only by an element contained in the group consisting ofgroup III elements Ga, Al, and In and group V element As. As a specificexample, the cladding layer 11 is an AlGaN layer, the active layer 12has a multiple quantum well structure (barrier layer: InGaN/well layer:InGaN), the basic layer 15 a of the phase modulation layer 15A is GaN,the modified refractive index region 15 b is a hole, the cladding layer13 is an AlGaN layer, and the contact layer 14 is a GaN layer.

Note that the same conductivity type as that of the semiconductorsubstrate 10 is imparted to the cladding layer 11, and a conductivitytype opposite to that of the semiconductor substrate 10 is imparted tothe cladding layer 13 and the contact layer 14. In one example, thesemiconductor substrate 10 and the cladding layer 11 are n-type, and thecladding layer 13 and the contact layer 14 are p-type. When the phasemodulation layer 15A is provided between the active layer 12 and thecladding layer 11, the phase modulation layer 15A has the sameconductivity type as that of the semiconductor substrate 10. On theother hand, when the phase modulation layer 15A is provided between theactive layer 12 and the cladding layer 13, the phase modulation layer15A has a conductivity type opposite to that of the semiconductorsubstrate 10. The impurity concentration is, for example, 1×10¹⁷ to1×10²¹/cm³. The phase modulation layer 15A and the active layer 12 areintrinsic (i-type) not intentionally doped with any impurity, and theirimpurity concentration is 1×10¹⁵/cm³ or less.

The thickness of the cladding layer 11 is 1×10³ to 3×10³ (nm), and inone example, it is 2×10³ (nm). The thickness of the active layer 12 is10 to 100 (nm), and in one example, it is 30 (nm). The thickness of thephase modulation layer 15A is 50 to 200 (nm), and in one example, it is100 (nm). The thickness of the cladding layer 13 is 1×10³ to 3×10³ (nm),and in one example, it is 2×10³ (nm). The thickness of the contact layer14 is 50 to 500 (nm), and in one example, it is 200 (nm).

In the above-described structure, the modified refractive index region15 b is a hole, but the modified refractive index region 15 b may beformed by embedding a semiconductor having a refractive index differentfrom that of the basic layer 15 a in the hole. In that case, forexample, the holes of the basic layer 15 a may be formed by etching. Thesemiconductor may be embedded in the holes using a metal organic vaporphase epitaxy method, a sputtering method, or an epitaxial method.Further, after the modified refractive index region 15 b is formed byembedding a semiconductor in the holes of the basic layer 15 a, the samesemiconductor as the modified refractive index region 15 b may befurther deposited thereon. In the case where the modified refractiveindex region 15 b is a hole, an inert gas such as argon, nitrogen, orhydrogen or air may be sealed in the hole.

The antireflection film 19 is made of a dielectric single layer filmsuch as silicon nitride (for example, SiN), silicon oxide (for example,SiO₂), or a dielectric multilayer film. As the dielectric multilayerfilm, for example, a film is applicable in which two or more types ofdielectric layers are laminated, and the dielectric layers are selectedfrom the group of dielectric layers such as titanium oxide (TiO₂),silicon dioxide (SiO₂), silicon monoxide (SiO), niobium oxide (Nb₂O₅),tantalum pentoxide (Ta₂O₅), magnesium fluoride (MgF₂), titanium oxide(TiO₂), aluminum oxide (Al₂O₃), cerium oxide (CeO₂), indium oxide(In₂O₃), and zirconium oxide (ZrO₂). For example, a film having athickness of λ/4 is laminated with an optical film thickness for lightof wavelength λ. The protective film 18 is an insulating film such as asilicon nitride (for example, SiN) or a silicon oxide (for example,SiO₂).

It is also possible to deform an electrode shape and emit laser lightfrom a surface of the contact layer 14. That is, when the opening 17 aof the electrode 17 is not provided, and the electrode 16 is open on asurface of the contact layer 14, the laser beam is emitted to theoutside from the surface of the contact layer 14. In this case, anantireflection film is provided in and around the opening of theelectrode 16.

FIG. 4 is a plan view of the phase modulation layer 15A. The phasemodulation layer 15A includes a basic layer 15 a formed of a firstrefractive index medium and a modified refractive index region 15 bformed of a second refractive index medium having a refractive indexdifferent from that of the first refractive index medium. Here, avirtual square lattice in the X-Y plane is set in the phase modulationlayer 15A. One side of the square lattice is parallel to the X axis, andthe other side is parallel to the Y axis. At this time, a square unitconstituent region R centered on the lattice point O of the squarelattice can be set two-dimensionally over a plurality of rows along theX axis and a plurality of rows along the Y axis. A plurality of themodified refractive index regions 15 b is provided one by one in eachunit constituent region R. The planar shape of the modified refractiveindex region 15 b is, for example, a circular shape. In each unitconstituent region R, the center of gravity G1 of the modifiedrefractive index region 15 b is disposed away from the nearest latticepoint O. Specifically, the X-Y plane is a plane orthogonal to thethickness direction (Z axis) of the laser element 2A illustrated inFIGS. 2 and 3 and coincides with one surface of the phase modulationlayer 15A including the modified refractive index region 15 b. Each unitconstituent region R constituting a square lattice is specified by acoordinate component x (an integer of 1 or more) in the X axis directionand a coordinate component y (an integer of 1 or more) in the Y axisdirection and represented as the unit constituent region R (x, y). Atthis time, the center of the unit constituent region R (x, y), that is,the lattice point is represented by O (x, y). Note that the latticepoint O may be located outside the modified refractive index region 15 bor may be included in the modified refractive index region 15 b.

In the case where the modified refractive index region 15 b is circular,the area S=π (D/2)² where its diameter is denoted by D. A ratio of thearea S of the modified refractive index region 15 b occupying within oneunit constituent region R is defined as a filling factor (FF). The areaof one unit constituent region R is equal to the area in one unitlattice of a virtual square lattice.

As illustrated in FIG. 5, the unit constituent region R (x, y)constituting a square lattice are defined by s and t axes orthogonal toeach other at the lattice point O (x, y). Note that the s axis is anaxis parallel to the X axis, and the t axis is an axis parallel to the Yaxis. In this way, in the s-t plane defining the unit constituent regionR (x, y), an angle formed by the direction from the lattice point O (x,y) to the center of gravity G1 and the s axis is obtained by φ (x, y).When the rotation angle φ (x, y) is 0°, the direction of a vectorconnecting the lattice point O (x, y) and the center of gravity G1coincides with the positive direction of the s axis. Further, the lengthof the vector connecting the lattice point O (x, y) and the center ofgravity G1 is obtained by r (x, y). As an example, r (x, y) is constant(over the entire phase modulation layer 15A) in the entire unitconstituent region.

As illustrated in FIG. 4, in the phase modulation layer 15A, therotation angle φ (x, y) of the center of gravity G1 of the modifiedrefractive index region 15 b around the lattice point O (x, y) is setindependently for each unit constituent region R accordingly. Therotation angle φ (x, y) has a specific value in the unit constituentregion R (x, y), but it is not necessarily expressed by a specificfunction. That is, the rotation angle φ (x, y) is determined from aphase term of a complex amplitude obtained by converting a desiredoptical image to a wavenumber space and performing two-dimensionalinverse Fourier transform to a constant wave number range of thewavenumber space. When the complex amplitude distribution (the complexamplitude of each unit constituent region R) is obtained from a desiredoptical image, by applying an iterative algorithm such as theGerchberg-Saxton (GS) method generally used at the time of calculationof hologram generation, the reproducibility of a beam pattern isimproved.

FIG. 6 is a plan view of an example in which a refractive indexsubstantially periodic structure of FIG. 4 is applied only in a specificregion of a phase modulation layer. In the example of FIG. 6, asubstantially periodic structure (for example, the structure of FIG. 4)for emitting a target beam pattern is formed inside a square innerregion RIN. On the other hand, in an outer region ROUT surrounding theinner region RIN, a true circular modified refractive index region inwhich the position of the center of gravity coincides with a latticepoint position of the square lattice is disposed. For example, thefilling factor FF in the outer region ROUT is set to 12%. Further, thelattice spacing of the square lattice that is virtually set is the same(=a) both within the inner region RIN and inside the outside regionROUT. In the case of this structure, since the light is distributed alsoin the outer region ROUT, there is an advantage that it is possible tosuppress the occurrence of high frequency noise (so-called windowfunction noise) caused by abrupt change in light intensity in theperipheral part of the inner region RIN. In addition, light leakage inan in-plane direction can be suppressed, and a reduction in a thresholdcurrent can be expected.

FIG. 7 is a diagram for explaining the relationship between an opticalimage corresponding to the beam pattern output from the laser element 2Aand the distribution of the rotation angle φ (x, y) in the phasemodulation layer 15A. More specifically, it is studied about the Kx-Kyplane obtained by converting, to a wavenumber space, a plane (aninstallation surface of a design optical image expressed by coordinates(x, y, z) in the XYZ orthogonal coordinate system) on which an opticalimage is formed by the beam emitted from the laser element 2A. The Kxaxis and the Ky axis defining the Kx-Ky plane are orthogonal to eachother, and each of them corresponds to an angle with respect to a normaldirection when the emission direction of a beam is swung from the normaldirection of the main surface 10 a of the semiconductor substrate 10 tothe main surface 10 a in accordance with the above-described formulas(1) to (5). On this Kx-Ky plane, a specific region including a beampattern corresponding to an optical image includes M2 (an integer of 1or more)×N2 (an integer of 1 or more) image regions FR. Further, it isassumed that a virtual square lattice set on the X-Y plane on the phasemodulation layer 15A includes M1 (an integer of 1 or more)×N1 (aninteger of 1 or more) unit constituent regions R. Note that the integerM2 does not have to match the integer M1. Likewise, the integer N2 doesnot have to match the integer N1. At this time, a complex amplitude F(x, y) in the unit constituent region R (x,y) obtained by performingtwo-dimensional inverse Fourier transform to transform from each of theimage regions FR (k_(x), k_(y)) on the Kx-Ky plane specified by thecoordinate component k_(x) (an integer of from 0 to M2-1) in the Kx axisdirection and the coordinate component k_(y) (an integer of from 0 toN2-1) on the Ky axis direction to the unit constituent region R (x,y)specified by the coordinate component x (an integer of from 1 to M1) inthe X axis direction and the coordinate component y (an integer of from1 to N1) in the Y axis direction is obtained by the following formula(11) with j being an imaginary unit.

$\begin{matrix}{{F\left( {x,y} \right)} = {\sum\limits_{k_{x} = 0}^{{M\; 2} - 1}{\sum\limits_{k_{y} = 0}^{{N\; 2} - 1}{{{FR}\left( {k_{x},k_{y}} \right)}{\exp\left\lbrack {j\; 2{\pi\left( {{\frac{k_{x}}{M\; 2}x} + {\frac{k_{y}}{N\; 2}y}} \right)}} \right\rbrack}}}}} & (11)\end{matrix}$

In the unit constituent region R (x, y), where the amplitude term isdenoted by A (x, y), and the phase term is denoted by P (x, y), thecomplex amplitude F (x, y) is defined by the following formula (12).F(x,y)=A(x,y)×exp[jP(x,y)]  (12)

As illustrated in FIG. 7, in the range of the coordinate components x=1to M1 and y=1 to N1, the distribution of the amplitude term A (x, y)with the complex amplitude F (x, y) of the unit constituent region R (x,y) corresponds to the intensity distribution on the X-Y plane. Further,in the range of x=1 to M1 and y=1 to N1, the distribution of P (x, y) atthe complex amplitude F (x, y) in the unit constituent region R (x, y)corresponds to the phase distribution on the X-Y plane. The rotationangle φ (x, y) in the unit constituent region R (x, y) is obtained fromP (x, y) as will be described later and, within the range of thecoordinate components x=1 to M1 and y=1 to N1, the distribution of therotation angle φ (x, y) of the unit constituent region R (x, y)corresponds to the rotation angle distribution on the X-Y plane.

The center Q of the output beam pattern on the Kx-Ky plane is located onthe axis perpendicular to the main surface 10 a of the semiconductorsubstrate 10. FIG. 7 illustrates four quadrants having the center Q asthe origin. FIG. 7 illustrates, as an example, the case where an opticalimage is obtained in the first quadrant and the third quadrant, but itis also possible to obtain images in the second quadrant and the fourthquadrant, or in all the quadrants. In the present embodiment, asillustrated in FIG. 7, an optical image which is point-symmetrical tothe origin can be obtained. FIG. 7 illustrates, as an example, the casewhere a character “A” is obtained in the third quadrant and a pattern inwhich the character “A” is rotated by 180° is obtained in the firstquadrant. In the case of a rotationally symmetric optical image (forexample, a cross, a circle, a double circle, etc.), the images overlapand are observed as one optical image.

The beam pattern (optical image) output from the laser element 2A is anoptical image corresponding to a design optical image (original image)represented by at least one of a spot, a straight line, a cross, a linedrawing, a lattice pattern, a photograph, a stripe pattern, CG (computergraphics), and letters. Here, in order to obtain a desired opticalimage, the rotation angle φ (x, y) of the modified refractive indexregion 15 b in the unit constituent region R (x, y) is determined by thefollowing procedure.

As described above, in the unit constituent region R (x, y), the centerof gravity G1 of the modified refractive index region 15 b is arrangedin a state away from the lattice point O (x, y) by r (x, y). At thistime, the modified refractive index region 15 b is disposed in the unitconstituent region R (x, y) such that the rotation angle φ (x, y)satisfies the following relationship.φ(x,y)=C×P(x,y)+B

C: Proportional constant, for example 180°/π

B: Arbitrary constant, for example 0

Note that the proportional constant C and the arbitrary constant B arethe same for all the unit constituent regions R.

That is, when it is desired to obtain a desired optical image, anoptical image formed on the Kx-Ky plane projected on the wavenumberspace is transformed into the unit constituent region R (x, y) on theX-Y plane on the phase modulation layer 15A by two-dimensional inverseFourier transform, and the rotation angle φ (x,y) corresponding to thephase term P (x, y) of the complex amplitude F (x, y) is given to themodified refractive index region 15 b disposed in the unit constituentregion R (x,y). It should be noted that a far field pattern after thetwo-dimensional inverse Fourier transform of the laser beam may beformed into various shapes such as a single or a plurality of spotshapes, annular shapes, linear shapes, character shapes, double circularring shapes, and Laguerre Gaussian beam shapes. Since the beam patternis represented by wavenumber information in the wavenumber space (on theKx-Ky plane), in the case of a bitmap image or the like in which thetarget beam pattern is represented by two-dimensional positioninformation, two-dimensional inverse Fourier transform may be performedafter conversion to wavenumber information once.

As a method for obtaining the intensity distribution and the phasedistribution from the complex amplitude distribution on the X-Y planeobtained by the two-dimensional inverse Fourier transform, for example,the intensity distribution (the distribution of the amplitude term A (x,y) on the X-Y plane) can be calculated using the abs function ofMathWorks' numerical analysis software “MATLAB”. The phase distribution(the distribution of the phase terms P (x, y) on the X-Y plane) can becalculated using the angle function of MATLAB.

Here, the rotation angle distribution (the distribution of the rotationangle φ (x, y) on the X-Y plane) is obtained from the result of thetwo-dimensional inverse Fourier transform of an optical image, and whenthe arrangement of the modified refractive index region 15 b in each ofthe unit constituent regions R is determined, points to be noted incalculation by using general discrete two-dimensional inverse Fouriertransform or fast two-dimensional inverse Fourier transform will bedescribed. When an optical image before the two-dimensional inverseFourier transform (design optical image on a predetermined planeexpressed by coordinates (x, y, z) in the XYZ orthogonal coordinatesystem) is divided into four quadrants such as A1, A2, A3, and A4, asthe original image illustrated in FIG. 8A, the obtained beam pattern isa pattern illustrated in FIG. 8B. That is, in the first quadrant of thebeam pattern of FIG. 8B, a pattern obtained by overlapping a patternobtained by rotating the first quadrant of FIG. 8A by 180° and a patternof the third quadrant of FIG. 8A appears. In the second quadrant of thebeam pattern of FIG. 8B, a pattern obtained by overlapping a patternobtained by rotating the second quadrant of FIG. 8A by 180° and apattern in the fourth quadrant of FIG. 8A appears. In the third quadrantof the beam pattern of FIG. 8B, a pattern obtained by overlapping apattern obtained by rotating the third quadrant of FIG. 8A by 180° and apattern of the first quadrant of FIG. 8A appears. In the fourth quadrantof the beam pattern of FIG. 8B, a pattern obtained by overlapping apattern obtained by rotating the fourth quadrant of FIG. 8A by 180° anda pattern of the second quadrant of FIG. 8A appears.

Therefore, when a pattern having a value only in the first quadrant isused as an optical image (original optical image) before thetwo-dimensional inverse Fourier transform, the pattern of the firstquadrant of the original optical image appears in the third quadrant ofthe obtained beam pattern. On the other hand, in the first quadrant ofthe obtained beam pattern, a pattern obtained by rotating the firstquadrant of the original optical image by 180° appears.

Next, a preferable distance between the center of gravity G1 of themodified refractive index region 15 b and the lattice point O of thevirtual square lattice will be described. When the lattice spacing ofthe square lattice is denoted by a, the filling factor FF of themodified refractive index region 15 b is obtained as S/a². Here, S isthe area of the modified refractive index region 15 b in the X-Y plane.For example, in the case of a true circular shape, and obtained asS=π×(D/2)² using the diameter D of the true circle. In the case of asquare shape, S=LA² is given by using the length LA of one side of thesquare.

Hereinafter, specific three configurations of the phase modulation layer15A will be described. FIG. 9A is an image of an original pattern commonto each configuration, and is a character of “light” composed of 704×704pixels. At this time, the letter “light” exists in the first quadrant,and there are no patterns in the second quadrant to the fourth quadrant.FIG. 9B is an image obtained by extracting the intensity distribution bytwo-dimensional Fourier transform on FIG. 9A and is constituted byelements of 704×704. FIG. 9C is an image obtained by extracting a phasedistribution by performing two-dimensional Fourier transform on FIG. 9A,which is constituted by elements of 704×704. This also corresponds tothe angular distribution at the same time, and FIG. 9C shows thedistribution of the phase from 0 to 2π (rad) depending on the shade ofcolor. The black color part represents the phase 0 (rad).

FIG. 10A is an image indicating the first configuration of the phasemodulation layer 15A for realizing the phase distribution illustrated inFIG. 9C, the basic layer 15 a is illustrated in black, and the modifiedrefractive index region 15 b is illustrated in white. In this firstconfiguration, 704×704 modified refractive index regions 15 b areincluded, the planar shape of the modified refractive index region 15 bis a true circle, and the lattice spacing a of the square lattice is 284nm. FIG. 10A illustrates the case where the diameter D of the modifiedrefractive index region 15 b is 111 nm, and the distance r between thelattice point O of the virtual square lattice and the center of gravityG1 of the modified refractive index region 15 b is 8.52 nm. At thistime, the filling factor FF of the modified refractive index region 15 bis 12%, and the distance r is 0.03a. FIG. 10B is a predicted beampattern obtained by Fourier transforming the entire modified refractiveindex region.

FIG. 11 is a graph indicating the S/N ratio of an output beam patternaccording to the relationship between the filling factor FF and thedistance r(a) in the first configuration (sample 1) of the phasemodulation layer 15A, that is the intensity ratio of a desired beampattern and noise. FIG. 12 is a graph indicating the relationshipbetween the distance r(a) and the S/N ratio in the case of FIG. 11(sample 1 of the first configuration). In the case of this structure,when the distance r is 0.3a or less, S/N is higher than the case ofexceeding 0.3a, and when the distance r is 0.01a or more, S/N is higherthan the case where the distance r is 0. In particular, referring toFIG. 12, a peak of the S/N ratio exists within these numerical ranges.That is, from the viewpoint of improving the S/N ratio, the distance ris preferably 0≤r≤0.3a, more preferably 0.01a≤r≤0.3a, and still morepreferably 0.03a≤r≤0.25. However, even when r is smaller than 0.01a, abeam pattern can be obtained although the S/N ratio is small.

FIG. 13A is an image (second configuration of the phase modulation layer15A) indicating the arrangement of the modified refractive index region15 b for realizing the phase distribution illustrated in FIG. 9C, thebasic layer 15 a is illustrated in black, and the modified refractiveindex region 15 b is illustrated in white. In this second configuration,the planar shape of the modified refractive index region 15 b is asquare, the number of the modified refractive index regions 15 b, andthe lattice spacing a of the square lattice are set to be the same asthe first configuration. In FIG. 13A, the length L of one side of themodified refractive index region 15 b is 98.4 nm, and the distance rbetween the lattice point O of the virtual square lattice and the centerof gravity G1 of the modified refractive index region 15 b is 8.52 nm.At this time, the filling factor FF of the modified refractive indexregion 15 b is 12%, and the distance r is 0.03a. FIG. 13B is a predictedbeam pattern obtained by Fourier transforming the entire modifiedrefractive index region.

FIG. 14 is a graph indicating the S/N ratio of an output beam patternaccording to the relationship between the filling factor FF and thedistance r(a) in the second configuration (sample 2) of the phasemodulation layer, that is the intensity ratio of a desired beam patternand noise. FIG. 15 is a graph indicating the relationship between thedistance r(a) and the S/N ratio in the case of FIG. 14 (sample 2 of thesecond configuration). Even in the case of this structure, when thedistance r is 0.3a or less, S/N is higher than the case of exceeding0.3a, and when the distance r is 0.01a or more, S/N is higher than thecase where the distance r is 0. In particular, referring to FIG. 15, apeak of the S/N ratio exists within these numerical ranges. That is,from the viewpoint of improving the S/N ratio, the distance r ispreferably 0<r≤0.3a, more preferably 0.01a≤r≤0.3a, and still morepreferably 0.03a≤r≤0.25. However, even when r is smaller than 0.01a, abeam pattern can be obtained although the S/N ratio is small.

FIG. 16A is an image (third configuration of the phase modulation layer15A) indicating the arrangement of the modified refractive index region15 b for realizing the phase distribution illustrated in FIG. 9C, thebasic layer 15 a is illustrated in black, and the modified refractiveindex region 15 b is illustrated in white. In the third configuration,the planar shape of the modified refractive index region 15 b is a shapeobtained by overlapping two true circles shifted from each other, andthe center of gravity of one true circle is made to coincide with thelattice point O. The number of modified refractive index regions 15 band the lattice spacing a of the square lattice are set to be the sameas in the first configuration. FIG. 10A illustrates the case where thediameters of the two perfect circles are both 111 nm and the distance rbetween the center of gravity of the other true circle and the latticepoint O is 14.20 nm. At this time, the filling factor FF of the modifiedrefractive index region 15 b is 12%, and the distance r is 0.05a. FIG.16B is a predicted beam pattern obtained by Fourier transforming theentire modified refractive index region.

FIG. 17 is a graph indicating the S/N ratio of an output beam patternaccording to the relationship between the filling factor FF and thedistance r(a) in the third configuration (sample 3) of the phasemodulation layer 15A, that is a graph indicating the intensity ratio ofa desired beam pattern and noise. FIG. 18 is a graph indicating therelationship between the distance r(a) and the S/N ratio in the case ofFIG. 17 (sample 3 of the third configuration). Even in the case of thisstructure, when the distance r is 0.3a or less, S/N is higher than thecase of exceeding 0.3a, and when the distance r is 0.01a or more, S/N ishigher than the case where the distance r is 0. In particular, referringto FIG. 18, a peak of the S/N ratio exists within these numericalranges. That is, from the viewpoint of improving the S/N ratio, thedistance r is preferably 0<r≤0.3a, more preferably 0.01a≤r≤0.3a, andstill more preferably 0.03a≤r≤0.25. However, even when r is smaller than0.01a, a beam pattern can be obtained although the S/N ratio is small.

Note that in the case of FIG. 11 (sample 1), FIG. 14 (sample 2), andFIG. 17 (sample 3), the region where the S/N ratio exceeds 0.9, 0.6, 0.3is given by the following function. FF 3, FF 6, FF 9, FF 12, FF 15, FF18, FF 21, FF 24, FF 27, FF 30 in FIG. 12 (Sample 1), FIG. 15 (Sample2), and FIG. 18 (Sample 3) are respectively FF=3%, FF=6%, FF=9%, FF=12%,FF=15%, FF=18%, FF=21%, FF=24%, FF=27%, FF=30%.

(S/N is 0.9 or more in FIG. 11.)FF>0.03,r>0.06,r<−FF+0.23, andr>−FF+0.13

(S/N is 0.6 or more in FIG. 11.)FF>0.03,r>0.03,r<−FF+0.25, andr>−FF+0.12

(S/N is 0.3 or more in FIG. 11.)FF>0.03,r>0.02,r<−(⅔)FF+0.30, andr>−(⅔)FF+0.083

(S/N is 0.9 or more in FIG. 14.)r>−2FF+0.25,r<−FF+0.25, andr>FF−0.05

(S/N is 0.6 or more in FIG. 14.)FF>0.03,r>0.04,r<−(¾)FF+0.2375, andr>−FF+0.15

(S/N is 0.3 or more in FIG. 14.)FF>0.03,r>0.01,r<−(⅔)FF+⅓, andr>−(⅔)FF+0.10

(S/N is 0.9 or more in FIG. 17.)r>0.025,r>−(4/3)FF+0.20, andr<−( 20/27)FF+0.20

(S/N is 0.6 or more in FIG. 17)FF>0.03,r>0.02,r>−(5/4)FF+0.1625, andr<−( 13/18)FF+0.222

(S/N is 0.3 or more in FIG. 17.)FF>0.03,r>0.01,r<−(⅔)FF+0.30, andr>−(10/7)FF+ 1/7

In the structure described above, the material system, the filmthickness, and the layer configuration can be variously changed as longas it includes the active layer 12 and the phase modulation layer 15A.Here, for the so-called square lattice photonic crystal laser in whichthe perturbation from the virtual square lattice is 0, the scaling ruleholds. That is, when the wavelength becomes a constant α times, the samestanding wave state can be obtained by multiplying the entire squarelattice structure by α. Similarly, also in this embodiment, it ispossible to determine the structure of the phase modulation layer 15Aaccording to the scaling rule corresponding to the wavelength.Therefore, it is also possible to realize a laser element 2A thatoutputs visible light by using the active layer 12 that emits light suchas blue, green, and red, and by applying a scaling rule according to thewavelength.

In manufacturing the laser element 2A, each compound semiconductor layeris obtained by a metal organic chemical vapor deposition (MOCVD) method.A crystal growth is performed on a surface (001) of the semiconductorsubstrate 10, but it is not limited thereto. When the laser element 2A,in which AlGaN is used, is manufactured, a growth temperature of AlGaAsis 500° C. to 850° C., and the temperature has been set to 550 to 700°C. in the experiment. The following materials are used during growth:trimethylaluminum (TMA) as an Al material, trimethylgallium (TMG) andtriethylgallium (TEG) as a gallium material, arsine (AsH₃) as an Asmaterial, disilane (Si₂H₆) as a material for N-type impurities, anddiethyl zinc (DEZn) as a material for a P-type impurities. TMG andarsine are used for growth of GaAs, but TMA is not used. InGaAs ismanufactured by using TMG, trimethylindium (TMI), and arsine. Theinsulating film may be formed by sputtering a target with theconstituent material as a raw material.

That is, in the laser element 2A described above, an AlGaAs layer as then-type cladding layer 11, an InGaAs/AlGaAs multiple quantum wellstructure as the active layer 12, a GaAs layer as the basic layer 15 aof the phase modulation layer 15A is epitaxially grown one by one usingthe MOCVD (metal organic chemical vapor deposition) method on a GaAssubstrate as an N-type semiconductor substrate 10. Next, in order toperform alignment after epitaxial growth, a SiN layer is formed on thebasic layer 15 a by a PCVD (plasma CVD) method, and then a resist isformed on the SiN layer. Further, the resist is exposed and developed,the SiN layer is etched using the resist as a mask, and an alignmentmark is formed in a state where a part of the SiN layer is left.Remaining resist is removed.

Next, another resist is applied to the basic layer 15 a, and atwo-dimensional fine pattern is drawn on the resist with an electronbeam drawing apparatus with reference to the alignment mark. Atwo-dimensional fine pattern is formed on the resist by developing theresist after drawing. Thereafter, using the resist as a mask, thetwo-dimensional fine pattern is transferred onto the basic layer 15 a bydry etching, and the resist is removed after the formation of holes. Thedepth of the hole is, for example, 100 nm. These holes are used as themodified refractive index regions 15 b. Alternatively, in these holes,compound semiconductors (AlGaAs) to be the modified refractive indexregions 15 b are regrown to more than the depth of the holes. When thehole is the modified refractive index region 15 b, a gas such as air,nitrogen, or argon may be sealed in the hole. Next, an AlGaAs layer asthe cladding layer 13 and a GaAs layer as the contact layer 14 aresequentially formed by MOCVD, and electrodes 16 and 17 are formed by avapor deposition method or a sputtering method. Further, as necessary,the protective film 18 and the antireflection film 19 are formed bysputtering or the like.

In the case where the phase modulation layer 15A is provided between theactive layer 12 and the cladding layer 11, the phase modulation layer15A may be formed on the cladding layer 11 before the formation of theactive layer 12. The lattice spacing a of the virtual square lattice isa degree obtained by dividing a wavelength by an equivalent refractiveindex and is set to about 300 nm, for example.

In the case of a square lattice of a lattice interval a, when unitvectors of an orthogonal coordinate are assumed to be x and y, basicparallel vectors are assumed to be a₁=ax, a₂=ay. A basic reciprocallattice vectors with respect to the parallel vectors a₁, a₂ are assumedto be b₁=(2π/a)y, b₂=(2π/a)x. When the wave number vector of the waveexisting in the lattice is k=nb₁+mb₂ (n, m is an arbitrary integer), thewave number k exists at a F point. In particular, when the size of awave number vector is equal to the size of a basic reciprocal latticevector, a resonance mode (standing wave in the X-Y plane) where thelattice spacing a is equal to the wavelength A, is obtained. In thepresent embodiment, oscillation in such a resonance mode (standing wavestate) is obtained. Considering a TE mode in which an electric field ispresent in a plane parallel to the square lattice, there are four modesdue to the symmetry of the square lattice in the standing wave state inwhich the lattice spacing and the wavelength are equal as describedabove. In the present embodiment, a desired beam pattern can besimilarly obtained in oscillation in any mode of in these four standingwave states.

Note that the standing wave in the phase modulation layer 15A isscattered by the hole shape and the wavefront obtained in a verticaldirection to the wavefront is phase-modulated, whereby a desired beampattern can be obtained. Therefore, a desired beam pattern can beobtained even without a polarizing plate. This beam pattern is not onlya pair of single peak beams (spots) but also can be a vector beam of acharacter shape or two or more identical shape spot groups or a vectorbeam in which the phase and the intensity distribution are spatiallyuneven.

A refractive index of the basic layer 15 a is preferably 3.0 to 3.5. Arefractive index of the modified refractive index region 15 b ispreferably 1.0 to 3.4. The average diameter of each modified refractiveindex region 15 b in the hole of the basic layer 15 a is, for example,38 nm to 76 nm. As the size of this hole changes, the diffractionintensity in the Z axis direction changes. This diffraction efficiencyis proportional to the optical coupling coefficient κ1 represented bythe first order coefficient when the shape of the modified refractiveindex region 15 b is Fourier transformed. The optical couplingcoefficient is described in, for example, K. Sakai et al., “Coupled-WaveTheory for Square-Lattice Photonic Crystal Lasers With TE Polarization,IEEE J. Q. E. 46, 788-795 (2010)”.

Subsequently, the light shielding member 3 illustrated in FIG. 1 will bedescribed in detail. The light shielding member 3 is, for example,supported by a housing that houses the laser element 2A, or is aplate-shaped member that constitutes a part of the housing.Alternatively, the light shielding member 3 may be formed directly onthe laser element 2A. The light shielding member 3 is disposed such thatpart of the light shielding member 3 crosses an axis orthogonal to thecenter of gravity of the light emitting surface 2 b of the laser element2A, that is, the Z axis illustrated in FIG. 1. One plate surface of thelight shielding member 3 faces the light emitting surface 2 b of thelaser element 2A. More specifically, this axis passes through the centerof the light emitting surface 2 b (the position of the center of gravityof the rectangular light emitting surface 2 b), that is, the center ofthe opening 17 a. From the laser element 2A, zero order light is outputalong this axis, that is, along the normal direction of the lightemitting surface 2 b.

FIGS. 19A to 19C are examples of beam patterns (optical images) outputfrom the laser element 2A. The center of each of FIGS. 19A to 19Ccorresponds to the axis orthogonal to the light emitting surface 2 b ofthe laser element 2A. As illustrated in FIGS. 19A to 19C, the opticalimage output from the light emitting surface 2 b includes zero orderlight B1 appearing as a bright spot on the axis and a first opticalimage portion B2 output in a first direction inclined to the axis, and asecond optical image portion B3 which is output in a second directionsymmetrical to the axis and which is rotationally symmetrical to thefirst optical image portion B2 with respect to the axis. Typically, thefirst optical image portion B2 is output in the first quadrant in theX-Y plane, and the second optical image portion B3 is output in thethird quadrant in the X-Y plane.

The light shielding member 3 of the present embodiment is disposed so asto pass through a desired optical image (for example, the first opticalimage portion B2) out of such optical images and at least shield thezero order light B1 appearing as a bright spot. More preferably, thelight shielding member 3 further shields the second optical imageportion B3 which is not the desired optical image. The light shieldingmember 3 may absorb the zero order light and the second optical imageportion B3 by including a light absorbing material on at least a surfaceon the laser element 2A side. In addition, the light shielding member 3may transmit light of another wavelength light as long as emissionwavelength light of the laser element 2A is shielded. Examples of aconstituent material of the light shielding member 3 include a metalthin film such as Au, Ti, Cr, and Al. Examples of a light absorbingmaterial include a cyanine dye, a phthalocyanine compound, anaphthalocyanine compound, a nickel dithiolene complex, a squaryliumdye, a quinone compound, a diimmonium compound, an azo compound,lanthanum hexaboride, cesium tungsten oxide, ITO, and antimony oxideTin.

Here, a preferable distance between the light shielding member 3 and thelight emitting surface 2 b in the Z axis direction and a preferableposition of the light shielding member 3 in the X-Y plane will beexamined in detail. As a preferable range of the light shielding member3, a range of a so-called far field pattern (Fraunhofer diffractionarea) is conceivable. However, the range of the Fraunhofer diffractionregion in the Z axis direction is obtained as z>L²/λ, where L is themaximum width of the opening 17 a, and λ is the wavelength (EugeneHecto, “Hect Optics II” page 244). Assuming that the width L of theopening 17 a is 400 μm, and the wavelength λ is 940 nm, z>170 mm.Further, when the width L is 200 μm, and λ is 940 nm, z>42 mm. In anycase, the far-field pattern is located at a distance of severalcentimeters or more from the light emitting surface 2 b, and it may bedifficult to dispose the light shielding member 3 at such a distantposition on the laser element 2A having a side length of less than 1 mm.Therefore, the present inventor has studied to provide the lightshielding member 3 at a position closer to the light emitting surface 2b.

Approximations are used in the so-called Fresnel diffraction image andFraunhofer diffraction image calculation formulas, and the range ofapplicable distance is each limited. Therefore, as will be describedbelow, the present inventor has calculated a diffraction image at thedistance z from the light emitting surface 2 b without approximation(the following formula (13)). The conditions used for the diffractioncalculation have been set as indicated in FIG. 20. That is, how thelight generated from the portion of the phase modulation layer 15A wherelight emission is obtained, that is, the portion corresponding to theelectrode 16 in the phase modulation layer 15A diffracts is calculated.In the example of FIG. 20, the opening H of the mask 100 corresponds tothe portion corresponding to the electrode 16 in the phase modulationlayer 15A. Hereinafter, a width of the opening H is referred to as anopening size (electrode size). In addition, the firstRayleigh-Sommerfeld solution (Joseph W. Goodman “Fourier Optics” section3.5) of Huygens-Fresnel principle has been used in the calculation of adiffraction image. In order to reproduce the zero order light, aconstant value has been superimposed on the entire complex amplitudedistribution on the light emitting surface 2 b.

$\begin{matrix}{{U\left( P_{0} \right)} = {\frac{1}{j\;\lambda}{\int{\int_{\Sigma}^{\;}{{U\left( P_{1} \right)}\frac{\exp\left( {jkr}_{01} \right)}{r_{01}}\cos\mspace{11mu}\theta\;{ds}}}}}} & (13)\end{matrix}$

In the above formula (13), U(P) represents a complex amplitude at acertain position P, P₀ represents a position of an observation point atwhich a diffraction image is obtained, P₁ represents a position of theopening H (that is, a portion of the phase modulation layer 15Acorresponding to the electrode 16), λ represents the wavelength of aplane wave, Σ represents the area of an opening, k represents awavenumber, r₀₁ represents a distance between a point on a surface ofthe opening and a point on a diffracted image (that is, the length of avector r₀₁). Here, the vector n represents a unit vector perpendicularto the opening H. Note that P₀ with a tilde “˜” in FIG. 20 is a pointset for convenience of calculation, it is at a symmetrical position onthe opposite side to P₀ and P₁, and its phase is 180° different from P₀.

FIG. 21A is a view of a target image used for the above diffractioncalculation. Further, FIGS. 21B and 21C are views illustrating a phasedistribution in the phase modulation layer 15A in the case of thelattice spacing a=282 nm, 141 nm, with shade of color. Since the numberof elements of a target image is 256×256, the number of elements of aphase distribution in the phase modulation layer 15A is also 256×256 inboth FIGS. 21B and 21C. However, when the lattice spacing a is 282 nm,the opening size (electrode size) is 72.2 μm on one side, and when thelattice spacing a is 141 nm, the opening size (electrode size) is 36.1μm on one side, reflecting the difference in lattice spacing.

FIG. 22 is a graph indicating the above-described calculation result andindicates correlation between a distance d and a distance z in the casewhere a distance between one end on the Z axis side of the diffractionimage on a diffraction image surface and the Z axis is denoted by d(μm), and a distance between the diffraction image surface and the lightemitting surface 2 b is denoted by z (μm). FIGS. 23 to 27 illustrate apart of the diffraction image which is the basis of this graph. FIG. 23illustrates the case where the number of elements of the phasedistribution is 128×128, the lattice spacing a=282 nm, one side of theopening size (electrode size) is 36.1 μm, and the wavelength λ=940 nm.FIG. 24 illustrates the case where the number of elements of the phasedistribution is 256×256, the lattice spacing a=282 nm, one side of theopening size (electrode size) is 72.2 and the wavelength λ=940 nm. FIG.25 illustrates the case where the number of elements of the phasedistribution is 512×512, the lattice spacing a=282 nm, one side of theopening size (electrode size) is 144.4 μm, and the wavelength λ=940 nm.FIG. 26 illustrates the case where the number of elements of the phasedistribution is 384×384, the lattice spacing a=282 nm, one side of theopening size (electrode size) is 108.3 μm, and the wavelength λ=940 nm.FIG. 27 illustrates the case where the number of elements of the phasedistribution is 1024×1024, the lattice spacing a=282 nm, one side of theopening size (electrode size) is 288.8 μm, and the wavelength λ=940 nm.

Referring to FIG. 22, irrespective of the opening size (electrode size)L, it can be seen that the distance d and the distance z are roughlyproportional to each other. Further, FIG. 28 is a graph indicating thecorrelation between the product (d×L) of the distance d and the openingsize (electrode size) L and the distance z. Referring to FIG. 28, it canbe seen that the product (d×L) and the distance z are roughlyproportional to each other. From the above, the following formula (14)holds.

$\begin{matrix}{d \propto \frac{z}{L}} & (14)\end{matrix}$

Based on this fact, FIG. 29 indicates a schematic diagram of thepositional relationship between the light emitting surface 2 b and thelight shielding member 3 on a reference plane RP (refer to FIG. 1)including the Z axis. In FIG. 29, the zero order light B1 is emittedfrom the light emitting surface 2 b of the laser element 2A along the Zaxis direction perpendicular to the light emitting surface 2 b, and fromthe light emitting surface 2 b, a desired first optical image portion B2is emitted in the direction (inclined direction) inclined to the Z axisdirection. The light shielding member 3 is arranged so as to shield allof the zero order light B1 and pass through all of the first opticalimage portion B2.

FIG. 30 is an enlarged diagram of the vicinity of an intersection V ofan Z-axis side edge of the first optical image portion B2 and the firstoptical image portion B2 side edge of the zero order light B1. Here, atriangle DL illustrated in FIG. 30 is focused. The triangle DL is aright triangle, a side DL1 is a line segment extending from one end 2 cof the light emitting surface 2 b in parallel to the Z axis, a side DL2is a line segment extending perpendicularly to the Z axis from theintersection V to the side DL1, and an oblique side DL3 is a linesegment connecting the one end 2 c of the light emitting surface 2 b andthe intersection V. Focusing on this triangle DL, the followingexpression (15) holds.

$\begin{matrix}{{\tan\;\theta_{PB}} = \frac{\frac{1}{2}\left( {W_{z} + L} \right)}{z_{sh}}} & (15)\end{matrix}$

Further, when the above formula (15) is modified, the following formula(16) is obtained. However, W_(z) is given by the following formula (17).

$\begin{matrix}{z_{sh} = \frac{W_{z} + L}{2\tan\;\theta_{PB}}} & (16) \\{{W_{Z} = {\frac{4\lambda}{\pi\; L}z\mspace{14mu}\left( {{{when}\mspace{14mu} z} \geq z_{0}} \right)}}{W_{Z} = {\sqrt{2}L\mspace{14mu}\left( {{{when}\mspace{14mu} z} < z_{0}} \right)}}} & (17)\end{matrix}$

Here, W_(z) represents the beam width (defined on the reference plane RPincluding the Z axis) of the zero order light B1 at the distance z, Lrepresents the width of the light emitting surface 2 b (refer to FIG.29) defined on the reference plane RP, θ_(PB) represents an angle (referto FIG. 30) formed by the Z axis side edge of the first optical imageportion B2 and the Z axis on the reference plane RP, and λ representsthe emission wavelength of the active layer 12. Also, z₀ in the aboveformula (17) represents the Rayleigh region and is derived by thefollowing formula (18).

$\begin{matrix}{z_{0} = {\frac{\pi}{\lambda}\left( \frac{L}{2} \right)^{2}}} & (18)\end{matrix}$

Therefore, it is preferable that the distance z from the light emittingsurface 2 b to the light shielding member 3 is longer than z_(sh)defined by the above formula (16). Thereby, the light shielding member 3can be disposed at a position where the zero order light B1 and thefirst optical image portion B2 are separated (that is, farther away fromthe intersection V). Further, it is preferable that the distance Wa(refer to FIG. 29) from the Z axis to the edge 3 c of the lightshielding member 3 is longer than half of the beam width W_(z) definedby the above formula (17). Thereby, the edge 3 c of the light shieldingmember 3 can be disposed between the zero order light B1 and the firstoptical image portion B2.

Here, the above formula (17) will be supplemented. FIG. 31 is a graphindicating a change in the beam radius at the beam waist of a Gaussianbeam. In this study, the zero order light B1 is regarded as a Gaussianbeam. The beam radius W(z) of the Gaussian beam is obtained by thefollowing formula (19).

$\begin{matrix}{{W(z)} = {W_{0}\left\lbrack {1 + \left( \frac{z}{z_{0}} \right)^{2}} \right\rbrack}^{\frac{1}{2}}} & (19)\end{matrix}$

Where W₀ is a beam waist radius. Further, z₀ is a Rayleigh region and isobtained by the following formula (20).

$\begin{matrix}{z_{0} = {\frac{\pi}{\lambda}W_{0}^{2}}} & (20)\end{matrix}$

The beam radius W(z) gradually increases as z increases, reaches √2W₀when z=z₀, and continues to monotonically increase with z. When z issufficiently larger than z₀, the first term of the above formula (19) isignored, and a linear relationship expressed by the following formula(21) is obtained. Note that θ₀ is a beam angle at a distance (refer toFIG. 31).

$\begin{matrix}{{{W(z)} \approx {\frac{W_{0}}{z_{0}}z}} = {\theta_{0}z}} & (21)\end{matrix}$

Here, since the relationship represented by the following formula (22)is obtained from the above formula (20), the beam angle θ₀ is expressedby the following formula (23). In other words, the beam angle θ₀ at adistance is proportional to the wavelength λ and inversely proportionalto the beam waist diameter W₀.

$\begin{matrix}{W_{0} = \left( \frac{\lambda\; z_{0}}{\pi} \right)^{\frac{1}{2}}} & (22) \\{\theta_{0} = \frac{\lambda}{\pi\; W_{0}}} & (23)\end{matrix}$

Based on the above, the beam diameter of the zero order light B1 will beconsidered. When the length of one side of the electrode 17 is denotedby L, and the wavelength is denoted by λ, the beam radius R1 satisfiesthe following formula (25) when the distance z satisfies the followingformula (24).

$\begin{matrix}{z < {\frac{\pi}{\lambda}\left( \frac{L}{2} \right)^{2}}} & (24) \\\left\lbrack {25} \right\rbrack & \; \\{{R\; 1} < \frac{L}{\sqrt{2}}} & (25)\end{matrix}$

Further, when the distance z becomes larger than the right side of theabove formula (24), the beam radius R1 satisfies the following formula(26).

$\begin{matrix}{{R\; 1} = {\frac{2\lambda}{\pi\; L}z}} & (26)\end{matrix}$

FIGS. 32A to 32D and FIGS. 33A to 33D are plan views illustratingconcrete examples of the arrangement of the light shielding members 3.In these figures, a range E indicated by a broken line represents anirradiation range of the zero order light B1. The plane shape of theirradiation range E is a square, the length of one side thereof isW_(z), and the center thereof is located on the Z axis (the origin ofthe Xs-Ys plane parallel to the X-Y plane). In any of the embodiments,the light shielding member 3 overlaps the Z axis, the edge 3 c of thelight shielding member 3 is separated from the Z axis by the distanceW_(z)/2, and the light shielding member 3 is disposed so as tocompletely cover the irradiation range E of the zero order light B1.

In FIG. 32A, the light shielding member 3 is arranged so as to entirelycover the third quadrant and the fourth quadrant. Such an arrangement iseffective when the unnecessary second optical image portion B3 (refer toFIGS. 19A to 19C) exists in the third quadrant or the fourth quadrant(or both). Further, in FIG. 32B, the light shielding member 3 isarranged so as to entirely cover the first quadrant and the secondquadrant. Such an arrangement is effective when the unnecessary secondoptical image portion B3 exists in the first quadrant or the secondquadrant (or both). Further, in FIG. 32C, the light shielding member 3is arranged so as to entirely cover the second quadrant and the thirdquadrant. Such an arrangement is effective when the unnecessary secondoptical image portion B3 exists in the second quadrant or the thirdquadrant (or both). Further, in FIG. 32D, the light shielding member 3is arranged so as to entirely cover the first quadrant and the fourthquadrant. Such an arrangement is effective when the unnecessary secondoptical image portion B3 exists in the first quadrant or the fourthquadrant (or both).

Further, in FIG. 33A, the light shielding member 3 is arranged so as toentirely cover the first quadrant. Such an arrangement is effective whenthe unnecessary second optical image portion B3 exists in the firstquadrant. Further, in FIG. 33B, the light shielding member 3 is arrangedso as to entirely cover the second quadrant. Such an arrangement iseffective when the unnecessary second optical image portion B3 exists inthe second quadrant. Further, in FIG. 33C, the light shielding member 3is arranged so as to entirely cover the third quadrant. Such anarrangement is effective when the unnecessary second optical imageportion B3 exists in the third quadrant. Further, in FIG. 33D, the lightshielding member 3 is arranged so as to entirely cover the fourthquadrant. Such an arrangement is effective when the unnecessary secondoptical image portion B3 exists in the fourth quadrant.

The effects obtained by the light emitting device 1A according to thepresent embodiment having the above configuration will be described. Inthe laser element 2A, the phase modulation layer 15A optically coupledto the active layer 12 has the basic layer 15 a and a plurality of themodified refractive index regions 15 b having different refractiveindices from that of the basic layer 15 a. In each of the unitconstituent regions R constituting a virtual square lattice, the centerof gravity G1 of the modified refractive index region 15 b is disposedaway from the lattice point O (the center of the unit constituent regionRno) and the direction of a vector from the lattice point O to thecenter of gravity G1 is individually set for each modified refractiveindex region 15 b. In such a case, the phase of a beam changes inaccordance with the direction of a vector from the lattice point O tothe center of gravity G1, that is, the angular position of the center ofgravity G1 around the lattice point O. That is, only by changing theposition of the center of gravity G1, it is possible to control thephase of the beams emitted from the modified refractive index regions 15b, and the beam pattern formed as a whole can have a desired shape.

That is, the laser element 2A is an S-iPM laser and can output anoptical image having an arbitrary shape along a normal direction of thelight emitting surface 2 b and an inclined direction having apredetermined inclination and a spread angle with respect to the normaldirection. Furthermore, in this light emitting device 1A, the lightshielding member 3 is provided so as to overlap at least the axis (thatis, the Z axis) orthogonal to the position of the center of gravity ofthe light emitting surface 2 b and allows the desired optical image topass therethrough and shields the zero order light B1. As a result, thezero order light B1 can be removed from the output of the S-iPM laser.

Further, as in the present embodiment, when the optical image includesthe first optical image portion B2 and the second optical image portionB3, the light shielding member 3 may further shield the second opticalimage portion B3. As a result, when the first optical image portion B2is a desired optical image, unnecessary second optical image portions B3can also be effectively removed.

Further, as in this embodiment, the light shielding member 3 may includea light absorbing material. When the light shielding member 3 reflectsthe zero order light B1, the reflected light again enters the laserelement 2A, which may affect the operation inside the laser element 2A.By including a light absorbing material in the light shielding member 3,it is possible to absorb the zero order light B1 and prevent the zeroorder light B1 from entering the laser element 2A again.

(First Modification)

FIG. 34 is a plan view of a phase modulation layer 15B according to amodification of the above-described embodiment. In addition to theconfiguration of the phase modulation layer 15A of the above-describedembodiment, the phase modulation layer 15B of the present modificationfurther includes a plurality of modified refractive index regions 15 c.Each of the modified refractive index regions 15 c includes a periodicstructure and is composed of a second refractive index medium having arefractive index different from that of the first refractive indexmedium of the basic layer 15 a. The modified refractive index region 15c is provided in one-to-one correspondence with the modified refractiveindex region 15 b. The center of gravity G2 of the modified refractiveindex region 15 c coincides with the lattice point O (the center of eachof the unit constituent regions R) of a virtual square lattice. Theplanar shape of the modified refractive index region 15 c is, forexample, circular. Like the modified refractive index region 15 b, themodified refractive index region 15 c may be a hole or may be formed byembedding a compound semiconductor in the hole. For example, even withthe configuration of the phase modulation layer as in the presentmodification, the effects of the above-described embodiment can besuitably exhibited.

(Second Modification)

FIGS. 35A to 35C and FIGS. 36A to 36B are plan views illustratingexamples of shapes in the X-Y plane of the modified refractive indexregion 15 b. In the example (patterns 1 to 5) illustrated in FIG. 35A,the shape in the X-Y plane of the modified refractive index region 15 bhas rotational symmetry. That is, the shape of each modified refractiveindex region in the X-Y plane is a perfect circle (pattern 1), square(pattern 2), regular hexagon (pattern 3), regular octagon (pattern 4),or regular hexadecagon (pattern 5). Compared with a rotationallyasymmetric figure, the figure of FIG. 35A has less influence even if thepattern is shifted in the rotation direction, and therefore highlyaccurate patterning is possible.

In the example (patterns 1 to 3) illustrated in FIG. 35B, the shape ofeach modified refractive index region in the X-Y plane has mirror imagesymmetry (line symmetry). That is, the shape of each modified refractiveindex region in the X-Y plane is a rectangle (pattern 1), an ellipse(pattern 2), a shape in which two circles or a part of an ellipseoverlaps (pattern 3). The lattice point O of the virtual square latticeis present outside these modified refractive index regions.

Compared with a rotationally asymmetric figure, the figure in FIG. 35Bcan clearly know the position of the line segment as a line symmetricreference, and therefore highly accurate patterning is possible.

In the examples (patterns 1 to 3) illustrated in FIG. 35C, the shape ofeach modified refractive index region in the X-Y plane is trapezoid(pattern 1), a shape in which the dimension in the short axis directionin the vicinity of one end portion along the long axis of an ellipse isdeformed so as to be smaller than the dimension of the short axis of thevicinity of the other end portion (egg type: pattern 2), or a shape inwhich one end portion along the long axis of an ellipse is deformed to asharpened end portion protruding along the long axis direction (teartype: pattern 3). The lattice point O of the virtual square lattice ispresent outside these modified refractive index regions. Even in thecase of the figure of FIG. 35C, the phase of a beam can be changed bythe position of the center of gravity of the modified refractive indexregion being displaced from the lattice point O of the virtual squarelattice by a distance r.

In the example (patterns 1 to 3) illustrated in FIG. 36A, the shape ofeach modified refractive index region in the X-Y plane has mirror imagesymmetry (line symmetry). That is, the shape of each modified refractiveindex region in the X-Y plane is a rectangle (pattern 1), an ellipse(pattern 2), a shape in which two circles or a part of an ellipseoverlaps (pattern 3). The lattice points O of the virtual square latticeare present inside these modified refractive index regions.

Compared with a rotationally asymmetric figure, the figure in FIG. 36Acan clearly know the position of the line segment as a line symmetricreference, and therefore highly accurate patterning is possible. Inaddition, since the distance r between the lattice point O of thevirtual square lattice and the position of the center of gravity of themodified refractive index region is small, it is possible to reduce theoccurrence of noise of the beam pattern.

In the examples (samples 1 to 4) illustrated in FIG. 36B, the shape ofeach modified refractive index region in the X-Y plane is an isoscelesright triangle (pattern 1), a trapezoid (pattern 2), a shape in whichthe dimension in the short axis direction in the vicinity of one endportion along the long axis of an ellipse is deformed so as to besmaller than the dimension in the short axis direction of the vicinityof the other end portion (egg type: pattern 3), or a shape in which oneend portion along the long axis of an ellipse is deformed to a sharpenedend portion protruding along the long axis direction (tear type: pattern4). The lattice points O of the virtual square lattice are presentinside these modified refractive index regions. Even in the case of thefigure of FIG. 36B, the phase of a beam can be changed by the positionof the center of gravity of the modified refractive index region beingdisplaced from the lattice point O of the virtual square lattice by thedistance r. In addition, since the distance r between the lattice pointO of the virtual square lattice and the position of the center ofgravity of the modified refractive index region is small, it is possibleto reduce the occurrence of noise of the beam pattern.

(Third Modification)

FIG. 37 illustrates a configuration of a light emitting device 1Baccording to a third modification. The light emitting device 1B includesa support substrate 6, a plurality of laser elements 2A arrangedone-dimensionally or two-dimensionally on the support substrate 6, alight shielding member 3B disposed to face a plurality of the laserelements 2A, and a drive circuit 4 for individually driving a pluralityof the laser elements 2A. The configuration of each laser element 2A isthe same as that of the above-described embodiment. However, each of aplurality of the laser elements 2A includes any one of a laser elementthat outputs an optical image in the red wavelength region, a laserelement that outputs an optical image in the blue wavelength region, anda laser element that outputs an optical image in the green wavelengthregion. The laser element for outputting the optical image in the redwavelength region includes, for example, a GaAs-based semiconductor. Thelaser element that outputs an optical image in the blue wavelengthregion and the laser element that outputs an optical image in the greenwavelength region include, for example, a nitride semiconductor. Thedrive circuit 4 is provided on the back side or the inside of thesupport substrate 6 and individually drives the respective laserelements 2A. The drive circuit 4 supplies a drive current to each of thelaser elements 2A according to a command from the control circuit 7.

The light shielding member 3B is a plate-shaped member provided so as tooverlap at least a plurality of axes (Z axis) orthogonal to each otherat a position of the center of gravity of each of the light emittingsurfaces 2 b of a plurality of the laser elements 2A. That is, in thepresent modification, the same number of light shielding members 3 asillustrated in FIG. 1 are disposed as a plurality of the laser elements2A, and these light shielding members 3 are integrated to form the lightshielding member 3B. The light shielding member 3B may be integratedwith a housing that houses the support substrate 6. Similarly to thelight shielding member 3 of the above-described embodiment, the lightshielding member 3B passes the first optical image portion B2 andshields the zero order light B1 among the optical images emitted fromthe respective laser elements 2A. In addition, the light shieldingmember 3B may further shield unnecessary second optical image portionsB3.

As in the present modification, the light shielding member 3B may beprovided on a plurality of the individually driven laser elements 2A,and only the desired optical image may be taken out from each laserelement 2A. In this case, it is possible to suitably realize a head updisplay or the like by appropriately driving required elements for amodule in which semiconductor light emitting elements corresponding to aplurality of patterns are aligned in advance. Further, as in the presentmodification, when a plurality of the laser elements 2A includes any oneof a laser element that outputs an optical image in a red wavelengthregion, a laser element that outputs an optical image in a bluewavelength region, a laser element that outputs an optical image in agreen wavelength region, a color head up display or the like can besuitably realized.

The semiconductor light emitting element according to the presentinvention is not limited to the above-described embodiment and can bevariously changed. For example, in the above-described embodiments andexamples, a laser element made of a GaAs-based, InP-based, andnitride-based (particularly GaN-based) compound semiconductor isexemplified, but the present invention is applicable to a laser elementmade of various semiconductor materials other than these.

REFERENCE SIGNS LIST

1A, 1B . . . light emitting device; 2A . . . laser element; 2 b . . .light emitting surface; 3 . . . light shielding member; 3B . . . lightshielding member; 3 c . . . edge; 4 . . . drive circuit; 6 . . . supportsubstrate; 7 . . . control circuit; 10 . . . semiconductor substrate;11, 13 . . . cladding layer; 12 . . . active layer; 14 . . . contactlayer; 15A, 15B . . . phase modulation layer; 15 a . . . basic layer; 15b, 15 c . . . modified refractive index region; 16, 17 . . . electrode;17 a . . . opening; 18 . . . protective film; 19 . . . antireflectionfilm; B1 . . . zero order light; B2 . . . first optical image portion;B3 . . . second optical image portion; G1, G2 . . . center of gravity; O. . . lattice point; and R . . . unit constituent region.

The invention claimed is:
 1. A light emitting device, comprising: asemiconductor light emitting element having a light emitting surface andconfigured to output an optical image having an arbitrary shape along anormal direction of the light emitting surface and an inclined directionhaving a predetermined inclination and a spread angle with respect tothe normal direction; and a light shielding member disposed such that anaxis orthogonal to the light emitting surface at a position of thecenter of gravity of the light emitting surface crosses a part of thelight shielding member, wherein the semiconductor light emitting elementincludes an active layer, a pair of cladding layers sandwiching theactive layer, and a phase modulation layer provided between the activelayer and one of a pair of the cladding layers and being opticallycoupled to the active layer, the light shielding member is disposed soas to pass through a specific optical image output in the inclineddirection among the optical images and shield zero order light output ina normal direction of the light emitting surface, the phase modulationlayer has a basic layer and a plurality of modified refractive indexregions each having a refractive index different from a refractive indexof the basic layer, and the phase modulation layer is configured suchthat: where, in an XYZ orthogonal coordinate system defined by a Z axiscoinciding with the normal direction and an X-Y plane including X and Yaxes which are orthogonal to each other and coincide with one surface ofthe phase modulation layer including a plurality of the modifiedrefractive index regions, a virtual square lattice constituted by M1 (aninteger of 1 or more)×N1 (an integer of 1 or more) unit constituentregions R each having a square shape is set on the X-Y plane, in theunit constituent region R (x, y) on the X-Y plane specified by acoordinate component x (an integer of from 1 to M1) in the X axisdirection and a coordinate component y (an integer of from 1 to N1) inthe Y axis direction, a center of gravity G1 of the modified refractiveindex region located in the unit constituent region R (x, y) is awayfrom a lattice point O (x, y) which is the center of the unitconstituent region R (x, y), and a vector from the lattice point O (x,y) to the center of gravity G1 is oriented in a specific direction,wherein in a state of satisfying the following first to sixthconditions: the first condition defined that coordinates (x, y, z) inthe XYZ orthogonal coordinate system satisfies a relationshiprepresented by the following formulas (1) to (3) with respect to aspherical coordinates (d1, θ_(tilt), θ_(rot)) defined by a length d1 ofa moving radius, an inclination angle θ_(tilt) from the Z axis, and arotation angle θ_(rot) from the X axis specified on the X-Y plane:x=d1 sin θ_(tilt) cos θ_(rot)  (1)y=d1 sin θ_(tilt) sin θ_(rot)  (2)z=d1 cos θ_(tilt)  (3), the second condition defined that letting a beampattern corresponding to the optical image output from the semiconductorlight emitting element is a set of bright points directed in directionsdefined by the angles θ_(tilt) and θ_(rot), the angles θ_(tilt) andθ_(rot) are converted into a coordinate value k_(x) on a Kx axiscorresponding to the X axis which is a normalized wave number defined bythe following formula (4) and a coordinate value k_(y) on a Ky axis,which is a specific wavenumber defined by the following formula (5),corresponds to the Y axis, and is orthogonal to the Kx axis:$\begin{matrix}{k_{x} = {\frac{a}{\lambda}\sin\;\theta_{tilt}\cos\;\theta_{rot}}} & (4) \\{k_{y} = {\frac{a}{\lambda}\sin\;\theta_{tilt}\sin\;\theta_{rot}}} & (5)\end{matrix}$ a: Lattice constant of vertical square lattice λ:Oscillation wavelength of semiconductor light emitting element, thethird condition defined that a specific wavenumber range including thebeam pattern includes M2 (an integer of 1 or more)×N2 (an integer of 1or more) image regions FR each having a square shape in a wavenumberspace defined by the Kx axis and the Ky axis, the fourth conditiondefined that, in the wavenumber space, a complex amplitude F (x, y)obtained by performing two-dimensional inverse Fourier transform totransform each of image regions FR (k_(x), k_(y)) specified by acoordinate component k_(x) (an integer of from 0 to M2−1) in the Kx axisdirection and a coordinate component k_(y) (an integer of from 0 toN2−1) in the Ky axis direction to the unit constituent region R (x,y) onthe X-Y plane is expressed by the following formula (6) with j being animaginary unit: $\begin{matrix}{{{F\left( {x,y} \right)} = {\sum\limits_{k_{x} = 0}^{{M\; 2} - 1}{\sum\limits_{k_{y} = 0}^{{N\; 2} - 1}{{{FR}\left( {k_{x},k_{y}} \right)}{\exp\left\lbrack {j\; 2{\pi\left( {{\frac{k_{x}}{M\; 2}x} + {\frac{k_{y}}{N\; 2}y}} \right)}} \right\rbrack}}}}},} & (6)\end{matrix}$ the fifth condition defined that the complex amplitude F(x, y) is defined by the following formula (7) while an amplitude termis denoted by A (x, y) and a phase term is denoted by P (x, y) in theunit constituent region R (x, y):F(x,y)=A(x,y)×exp[jP(x,y)]  (7), and the sixth condition defined thatthe unit constituent region R (x, y) is defined by an s-axis and at-axis which are parallel to the X-axis and the Y-axis and orthogonal atthe lattice point O (x, y), the phase modulation layer is configuredsuch that: in a state in which a line segment length r (x, y) from thelattice point O (x, y) to the center of gravity G1 of the correspondingmodified refractive index region is set to a common value in each of theM1×N1 unit constituent regions R, an angle φ (x, y) formed by a linesegment connecting the lattice point O (x, y) and the center of gravityG1 of the corresponding modified refractive index region and the s axissatisfies a relationship expressed by the following formula:φ(x,y)=C×P(x,y)+B C: proportional constant B: arbitrary constant, andthe corresponding modified refractive index region is disposed in theunit constituent region R (x, y).
 2. The light emitting device accordingto claim 1, wherein where a lattice constant of the virtual squarelattice is denoted by a, a distance r between the center of gravity G1of the modified refractive index region located in the unit constituentregion R (x, y) and the lattice point O (x, y) satisfies 0≤r≤0.3a. 3.The light emitting device according to claim 1, wherein where a distancefrom the light emitting surface to the light shielding member is denotedby z, a distance from the axis to a nearest end edge of the lightshielding member on a reference plane including the axis is denoted byWa, a beam width of zero order light at a point of the distance z on thereference surface is denoted by Wz, a width of the light emittingsurface defined on the reference plane is denoted by L, an angle formedby the axial line side edge of the specific optical image and the axison the reference plane is denoted by θ_(PB), and an emission wavelengthof the active layer is denoted by λ, the distance z is longer thanz_(sh) defined by the following formula (8): $\begin{matrix}{{z_{sh} = \frac{W_{z} + L}{2\tan\;\theta_{PB}}},} & (8)\end{matrix}$ the distance Wa is longer than half of W_(z) defined bythe following formula (9): $\begin{matrix}{{W_{Z} = {\frac{4\lambda}{\pi\; L}z\mspace{14mu}\left( {{{where}\mspace{14mu} z} \geq z_{0}} \right)}}{{W_{Z} = {\sqrt{2}L\mspace{14mu}\left( {{{where}\mspace{14mu} z} < z_{0}} \right)}},}} & (9)\end{matrix}$ and Z₀ of the formula (9) is a numerical value defined bythe following formula (10): $\begin{matrix}{z_{0} = {\frac{\pi}{\lambda}{\left( \frac{L}{2} \right)^{2}.}}} & (10)\end{matrix}$
 4. The light emitting device according to claim 1, whereinthe optical image includes a first optical image portion to be output ina first direction that is inclined with respect to the axis and a secondoptical image portion that is output in a second direction symmetricalto the first direction with respect to the axis and rotationallysymmetric with the first optical image portion with respect to the axis,and the light shielding member is arranged to further shield the secondoptical image portion.
 5. The light emitting device according to claim1, wherein the light shielding member includes a light absorbingmaterial.
 6. A light emitting device, comprising: a plurality ofsemiconductor light emitting elements each having a light emittingsurface and configured to output an optical image having an arbitraryshape along a normal direction of the light emitting surface and aninclined direction having a predetermined inclination and a spread anglewith respect to the normal direction, a light shielding member disposedsuch that a part of the light shielding member intersects each of axesorthogonal to the light emitting surface at a position of the center ofgravity of the light emitting surface of each of a plurality of thesemiconductor light emitting elements, and a drive circuit configured toindividually drive a plurality of the semiconductor light emittingelements, wherein each of a plurality of the semiconductor lightemitting elements includes an active layer, a pair of cladding layerssandwiching the active layer, and a phase modulation layer providedbetween the active layer and either a pair of the cladding layers andoptically coupled to the active layer, the light shielding member isdisposed so as to pass through a specific optical image output in theinclined direction among the optical images and to shield zero orderlight each output in the normal direction of the light emitting surface,in each of a plurality of the semiconductor light emitting elements, thephase modulation layer has a basic layer and a plurality of modifiedrefractive index regions each having a different refractive index from arefractive index of the basic layer, and the phase modulation layer, ineach of a plurality of the semiconductor light emitting elements, isconfigured such that: where, in an XYZ orthogonal coordinate systemdefined by a Z axis coinciding with the normal direction and an X-Yplane including X and Y axes which are orthogonal to each other andcoincide with one surface of the phase modulation layer including aplurality of the modified refractive index regions, a virtual squarelattice including M1 (an integer of 1 or more)×N1 (an integer of 1 ormore) unit constituent regions R each having a square shape is set onthe X-Y plane, in the unit constituent region R (x, y) on the X-Y planespecified by a coordinate component x (an integer of from 1 to M1) inthe X axis direction and a coordinate component y (an integer of from 1to N1) in the Y axis direction, the center of gravity G1 of the modifiedrefractive index region located in the unit constituent region R (x, y)is away from a lattice point O (x, y) which is the center of the unitconstituent region R (x, y), and a vector from the lattice point O (x,y) to the center of gravity G1 is oriented in a specific direction,wherein in a state of satisfying the following first to sixthconditions: the first condition defined that coordinates (x, y, z) inthe XYZ orthogonal coordinate system satisfies a relationshiprepresented by the following formulas (11) to (13) with respect to aspherical coordinates (d1, θ_(tilt), θ_(rot)) defined by a length d1 ofa moving radius, an inclination angle θ_(tilt) from the Z axis, and arotation angle θ_(rot) from the X axis specified on the X-Y plane:x=d1 sin θ_(tilt) cos θ_(rot)  (11)y=d1 sin θ_(tilt) sin θ_(rot)  (12)z=d1 cos θ_(tilt)  (13), the second condition defined that letting abeam pattern corresponding to the optical image output from thesemiconductor light emitting element is a set of bright points directedin directions defined by the angles θ_(tilt) and θ_(rot), the anglesθ_(tilt) and θ_(rot) are converted into a coordinate value k_(x) on a Kxaxis corresponding to the X axis which is a normalized wave numberdefined by the following formula (14) and a coordinate value k_(y) on aKy axis, which is a specific wavenumber defined by the following formula(15), corresponds to the Y axis, and is orthogonal to the Kx axis:$\begin{matrix}{k_{x} = {\frac{a}{\lambda}\sin\;\theta_{tilt}\cos\;\theta_{rot}}} & (14) \\{k_{y} = {\frac{a}{\lambda}\sin\;\theta_{tilt}\sin\;\theta_{rot}}} & (15)\end{matrix}$ a: Lattice constant of vertical square lattice λ:Oscillation wavelength of semiconductor light emitting element, thethird condition defined that a specific wavenumber range including thebeam pattern includes M2 (an integer of 1 or more)×N2 (an integer of 1or more) image regions FR each having a square shape in a wavenumberspace defined by the Kx axis and the Ky axis, the fourth conditiondefined that, in the wavenumber space, a complex amplitude F (x, y)obtained by performing two-dimensional inverse Fourier transform totransform each of image regions FR (k_(x), k_(y)) specified by acoordinate component k_(x) (an integer of from 0 to M2−1) in the Kx axisdirection and a coordinate component k_(y) (an integer of from 0 toN2−1) in the Ky axis direction to the unit constituent region R (x,y) onthe X-Y plane is expressed by the following formula (16) with j being animaginary unit: $\begin{matrix}{{{F\left( {x,y} \right)} = {\sum\limits_{k_{x} = 0}^{{M2} - 1}{\sum\limits_{k_{y} = 0}^{{N2} - 1}{F{R\left( {k_{x},k_{y}} \right)}{\exp\left\lbrack {j\; 2{\pi\left( {{\frac{k_{x}}{M2}x} + {\frac{k_{y}}{N2}y}} \right)}} \right\rbrack}}}}},} & (16)\end{matrix}$ the fifth condition defined that the complex amplitude F(x, y) is defined by the following formula (17) while an amplitude termis denoted by A (x, y) and a phase term is denoted by P (x, y) in theunit constituent region R (x, y):F(x,y)=A(x,y)×exp[jP(x,y)]  (17), and the sixth condition defined thatthe unit constituent region R (x, y) is defined by an s-axis and at-axis which are parallel to the X-axis and the Y-axis and orthogonal atthe lattice point O (x, y), the phase modulation layer is configuredsuch that: in a state in which a line segment length r (x, y) from thelattice point O (x, y) to the center of gravity G1 of the correspondingmodified refractive index region is set to a common value in each of theM1×N1 unit constituent regions R, an angle φ (x, y) formed by a linesegment connecting the lattice point O (x, y) and the center of gravityG1 of the corresponding modified refractive index region and the s axissatisfies a relationship expressed by the following formula:φ(x,y)=C×P(x,y)+B C: proportional constant B: arbitrary constant, andthe corresponding modified refractive index region is disposed in theunit constituent region R (x, y).
 7. The light emitting device accordingto claim 6, wherein each of a plurality of the semiconductor lightemitting elements includes any one of a semiconductor light emittingelement configured to output the optical image in a red wavelengthrange, a semiconductor light emitting element configured to output theoptical image in a blue wavelength range, and a semiconductor lightemitting element configured to output the optical image in a greenwavelength range.
 8. The light emitting device according to claim 6,wherein where a distance from the light emitting surface to the lightshielding member is denoted by z, a distance from the axis to a nearestend edge of the light shielding member on a reference plane includingthe axis is denoted by Wa, a beam width of zero order light at a pointof the distance z on the reference surface is denoted by W_(z), a widthof the light emitting surface defined on the reference plane is denotedby L, an angle formed by the axial line side edge of the specificoptical image and the axis on the reference plane is denoted by θ_(PB),and an emission wavelength of the active layer is denoted by λ, thedistance z is longer than z_(sh) defined by the following formula (18):$\begin{matrix}{{z_{sh} = \frac{W_{z} + L}{2\tan\;\theta_{PB}}},} & (18)\end{matrix}$ the distance Wa is longer than half of W_(z) defined bythe following formula (19): $\begin{matrix}\begin{matrix}{{W_{Z} = {\frac{4\lambda}{\pi L}z}}\;} & \left( {{{where}\mspace{14mu} z} \geq z_{0}} \right) \\{W_{Z} = {\sqrt{2}L}} & {\left( {{{where}\mspace{20mu} z} < z_{0}} \right),}\end{matrix} & (19)\end{matrix}$ and Z₀ of the formula (19) is a numerical value defined bythe following formula (20): $\begin{matrix}{z_{0} = {\frac{\pi}{\lambda}{\left( \frac{L}{2} \right)^{2}.}}} & (20)\end{matrix}$